Algebra and Trigonometry (4th Edition)

Chapter 6

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512515,625 ; An exponential function is defined as... more

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Recall exponential functions are in the form . ... more

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PrincipalInterest rate per yearNumber of times ... more

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Horizontal0 ; Recall that the exponential function... more

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Horizontal3 ; The function  has a horizontal ... more

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; Substitute the given  value into the function ... more

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; Substitute the given value for  and calculate... more

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; Substitute the given value for  and calculate... more

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; Substitute the given value for  and calculate... more

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Create a table of values. Plot the points. Sketch ... more

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Create a table of values. Plot the points. Sketch ... more

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Create a table of values. Plot the points. Sketch ... more

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Create a table of values. Plot the points. Sketch ... more

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Create a table of values. Plot the points. Sketch ... more

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Create a table of values. Plot the points. Sketch ... more

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Create a table of values or use the rules for ... more

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Begin by graphing . ; Consider we have and the ... more

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Here we have that both and have base values ... more

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Begin by graphing . Consider the value of the base... more

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; We know the point is on the graph, thus we can... more

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; We know the point passes through the graph, ... more

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; We know the point passes through the graph, ... more

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; We know the point passes through the graph, ... more

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Begin with the graph of . The graph of represents... more

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Begin with the graph . The graph of represents a ... more

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, ,   ; Draw the exponential shape of . ; Reflect ... more

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,  , ; Draw the exponential shape of . ; Reflect ... more

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, , ; Draw the exponential shape of . ; Obtain the... more

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 , , ; Draw the exponential shape of . ; Reflect ... more

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, , ; Draw the exponential shape of . ; Obtain the... more

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, , ; Draw the exponential shape of . ; Reflect ... more

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, , ; Draw the exponential shape of . ; Reflect ... more

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, , ; Draw the exponential shape of . ; Reflect ... more

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01234681001827642165121,000139278172919,68359,049... more

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0123468100116812561,2964,09610,0001416642564,09665... more

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The higher the value of , the quicker the graph ... more

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The higher the value of , the quicker the graph ... more

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Let . Now,  ; Find by substituting into the ... more

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; Determine the amount for each given time using... more

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; Determine the amount for each given interest ... more

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; Write the compound interest formula using: ... more

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$67,121.04 ; Write the compound interest formula ... more

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; Write the compound interest formula using: as ... more

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; Write the compound interest formula using: as ... more

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option (b) ; Write the as one-month payment under... more

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4 by 16 inches ; Since for every 10 units is 1 ... more

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principal ; The equation is called the ... more

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12.71823.1410.0504.113 ; Evaluate the given at ... more

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0.3680.01120.086 ; Evaluate the given at using ... more

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; Make a table of values of the given at the ... more

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; Evaluate the function at the given values of . ... more

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Domain: Range: Asymptote: ; Let . Write in terms ... more

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Domain: Range: Asymptote: ; Let . Write in terms ... more

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Domain: Range: Asymptote: ; Let . Write in terms ... more

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Domain: Range: Asymptote: ; Let . Write in terms ... more

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Domain: Range: Asymptote: ; Let . Write in terms ... more

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Domain: Range: Asymptote: ; Let . Write in terms ... more

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Domain: Range: Asymptote: ; Let . Write in terms ... more

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Domain: Range: Asymptote: ; Let . Write in terms ... more

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Domain: Range: Asymptote: ; Let . Write in terms ... more

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Domain: Range: Asymptote: ; Let . Write in terms ... more

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As increases without bound, the graph of ... more

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no local maximumlocal minimum value is 0.68 and it... more

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no local maximumlocal minimum value is 1.89 and it... more

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27.4 mg ; Substitute into the given equation, ... more

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1.6 ft ; Substitute into the given equation, then... more

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123456 ; Substitute and into the continuously ... more

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0.010.020.030.040.050.06 ; Substitute and into ... more

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Assign or determine the values for , , , and .Let... more

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Assign or determine the values for , , , and for ... more

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; The common logarithm, , is in base 10. Let . In... more

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9 ; The base of the log function refers to the ... more

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The graph of increases rapidly within , then ... more

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vertical ; Begin with the graph of . ; From the ... more

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vertical ; If a number is added to the input, , ... more

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form form ; The exponential form, , is equivalent... more

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form form ; The exponential form, , is equivalent... more

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Make a table of values for the given logarithmic ... more

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Make a table of values for the given logarithmic ... more

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Make a table of values for the given common ... more

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Make a table of values for the given common ... more

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; Determine the base of the given logarithmic ... more

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; Determine the base of the given logarithmic ... more

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; Determine the base of the given logarithmic ... more

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; Determine the base of the given logarithmic ... more

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Make a table of values for the given exponential ... more

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Make a table of values for the given exponential ... more

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Domain: Range: Asymptote: ; Draw the graph defined... more

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Domain: Range: Asymptote: ; Draw the graph defined... more

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Domain: Range: Asymptote: ; Draw the graph defined... more

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Domain: Range: Asymptote: ; Draw the graph defined... more

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Domain: Range: Asymptote: ; Draw the graph defined... more

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Domain: Range: Asymptote: ; Draw the graph defined... more

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Domain: Range: Asymptote: ; Draw the graph defined... more

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Domain: Range: Asymptote: ; Draw the graph defined... more

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Domain: Range: Asymptote: ; Draw the graph defined... more

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Domain: Range: Asymptote: ; Draw the graph defined... more

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Domain: Range: Asymptote: ; Draw the graph defined... more

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Domain: Range: Asymptote: ; Use the definition of ... more

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; Determine the domain of :Set the expression ... more

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; Determine the domain of : Set the expression ... more

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; Determine the domain of :Set the expression ... more

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; Determine the domain of :Set the expression ... more

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; Determine the domain of :Set the expression ... more

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; Determine at which is defined by setting the ... more

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Domain: Asymptotes: and Local Maximum: Local ... more

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Domain: Asymptotes: and Local Maximum: noneLocal ... more

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Domain: Asymptotes:  Local Maximum: noneLocal ... more

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Domain: Asymptotes:  Local Maximum: Local Minimum... more

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Domain: Asymptotes:  Local Maximum: noneLocal ... more

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Domain: Asymptotes:  Local Maximum: noneLocal ... more

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, domain: , domain:   ; Determine the domain and ... more

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, domain: , domain: ; Determine the domain and ... more

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, domain: , domain:   ; Determine the domain and ... more

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domain: domain: ; Determine the domain and range... more

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The growth rate of is slower than the growth rate... more

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mol/L ; Use for .Evaluate the given equation at .... more

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2602 years ; Use for .Evaluate the given equation... more

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43 hours ; Evaluate the given equation at . ; It ... more

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At :   yearsAt :   yearsAt :   years  ; Use for .... more

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hour ; Use for .Evaluate the given equation at ... more

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The index of difficulty becomes higher the shorter... more

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2 and 2 ; Substitute to find the value of .... more

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Let and then write this in exponential form . ... more

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Any number between 1,000 and 10,000 will have 4 ... more

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sum ; The first law of logarithms states that .... more

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difference ; The second law of logarithms states ... more

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exponent ; The third law of logarithms states . ... more

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; The second law of logarithms states that . ... more

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; The third law of logarithms states that . Apply... more

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4 ; The First law of logarithms states that . ; ... more

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3 ; The first law of logarithms states that . ; ... more

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2 ; The second law of logarithms states that . ; ... more

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1 ; The second law of logarithms states that . ... more

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1 ; The third law of logarithms states that .Apply... more

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; The third law of logarithms states that .Apply ... more

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; The third law of logarithms states that .Apply ... more

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; The third law of logarithms states that .Apply ... more

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3 ; The Second law of logarithm states that . ; ... more

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; The second law of logarithm states that . ; ... more

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200 ; The third law of logarithms states that .... more

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99 ; The third law of logarithms states that .... more

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4 ; The third law of logarithms states that .Apply... more

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200 ; The third law of logarithms states that .... more

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; The first law of logarithms states that .Apply ... more

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; The first law of logarithms states that .Apply ... more

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; The first law of logarithms states that .Apply ... more

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; First law of logarithm states that .Apply first... more

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; The third law of logarithms states that .Apply ... more

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; Rewrite the root as fractional exponent using ... more

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; The third law of logarithms states that .Apply ... more

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; Rewrite the root as an fractional exponent ... more

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; The first law of logarithms states that .Apply ... more

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; The first law of logarithms states that .Apply ... more

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; The second law of logarithms states that .Apply... more

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; The second law of logarithms states that .Apply... more

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; The second law of logarithms states that . ... more

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; The second law of logarithms states that .Apply... more

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; The second law of logarithms states that .Apply... more

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; The second law of logarithms states that .Apply... more

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; The second law of logarithms states that .Apply... more

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; The second law of logarithms states that .Apply... more

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; Rewrite the root as fractional exponent using ... more

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;  Rewrite the root as fractional exponent using ... more

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; Use to write the given logarithm as the sum of... more

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; Use to write the given logarithm as the ... more

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; Transform the radical expression into its ... more

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; Use to write the given logarithm as the ... more

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; Write the radical in rational exponent form.Use... more

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; Write the outermost radical in rational ... more

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; Use to write 2 as the exponent of 7, and then ... more

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; Use to write as the exponent of 5.Similarly, ... more

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; Use to write 2 as the exponent of .Similarly, ... more

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; Apply the law to the first term to write 3 as ... more

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; Rewrite each term using the law . ; Use to ... more

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; Use to write the given difference as the ... more

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; Use to write the sum of the first two terms as... more

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; Distribute by multiplying it by the ... more

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; Distribute to each term inside the brackets... more

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; Rewrite the second and the third terms using ... more

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; Use the formula to change the base of the ... more

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; Use the formula to change the base of the ... more

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; Use the formula to change the base of the ... more

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; Use the formula to change the base of the ... more

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; Use the formula to change the base of the ... more

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; Use the formula to change the base of the ... more

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; Use the formula to change the base of the ... more

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; Use the formula  to change the base of the ... more

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The base of a logarithm can be changed to using ... more

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All the graphs pass through the point .For , the ... more

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is a common logarithm with base . To obtain the ... more

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; Apply the formula to write each logarithm as a... more

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; Start with the LHS:Apply the power law of the ... more

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; Write the equation which describes the ... more

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; Evaluate .Write as and use the power law to ... more

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Let .To shrink the graph by a factor of , evaluate... more

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4 ; Rewrite the value on the right side of the ... more

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; Note that the expressions have the same bases. ... more

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; Rewrite the value on the right side of the ... more

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1 ; Rewrite the value on the right side of the ... more

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; Note that the expressions have the same bases. ... more

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; Note that the expressions have the same bases. ... more

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; Note that the expressions have the same bases. ... more

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; Note that the expressions have the same bases. ... more

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; Use the power rule of exponents to rewrite the... more

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; Use the power rule of exponents to rewrite the... more

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; Use the power rule of exponents to rewrite the... more

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; Use the exponent rule to rewrite the second ... more

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; Use the exponent rule to rewrite the second ... more

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; Factor out from the expression on the left ... more

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; Subtract from both sides of the equation then ... more

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; Factor out from each term on the left. Factor ... more

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; Factor out from each term on the left. ; ... more

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; Condense the expression on the left using the ... more

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; Condense the expression on the left using the ... more

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; Condense the expression on the right using the ... more

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; Condense the expression on the left using the ... more

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; Condense the expression on both sides using the... more

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; Condense the expression on both sides using the... more

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; Write the equation in exponential form. By ... more

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; Write the equation in exponential form. By ... more

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; Write the equation in exponential form. By ... more

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; Write the equation in exponential form. By ... more

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; Write the equation in exponential form. By ... more

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; Write the equation in exponential form. By ... more

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; Subtract 4 from both sides.Then multiply both ... more

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; Write the equation in exponential form. By ... more

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; Condense the expressions on the left using the ... more

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; Condense the expressions on the left using the ... more

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; Condense the expressions on the left using the ... more

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; Condense the expressions on the left using the ... more

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; Condense the expressions on the left using the ... more

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; Condense the expressions on the left using the ... more

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; Move all terms on the left by subtracting from... more

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, ; Enter and into a graphing utility and use ... more

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, ; Enter and into a graphing utility and use ... more

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, ; Enter and into a graphing utility and use ... more

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; Enter and into a graphing utility and use the... more

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; Enter and into a graphing utility and use the... more

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; Enter and into a graphing utility and use the... more

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, ; Enter and into a graphing utility and use ... more

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; Express as an exponential with the base . ; ... more

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; Raise to each sides of the given equation.... more

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or ; Determine at which the given inequality is ... more

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; Determine at which the given inequality is ... more

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; Take the common logarithm of each sides of the ... more

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; Take out the common factor in the given ... more

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; Write and interchange the variables and .Take... more

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; Write and interchange the variables and .Take... more

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; Write and interchange the variables and . ; ... more

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; Write and interchange the variables and . ; ... more

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; Use the logarithm product law, , to combine the... more

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,, ; Move all terms to one side of the equation to... more

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years ; Use the formula for compound interest ... more

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years ; Use the formula for compound interest ... more

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years ; To double the investment, multiply the ... more

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or ; Use the formula for compound interest with... more

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or days ; Use the given equation with .Divide ... more

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seconds ; Use the given equation with and divide... more

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A table of values for with consecutive -values is... more

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Taking the logarithm of both sides of the equation... more

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18 years ; Write the radioactive decay model ... more

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seconds or about minutes ; Write the radioactive... more

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149 hours ; Write the decay model  with , , and .... more

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3561 years ; Write the radioactive decay model ... more

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4362 years ; Write the radioactive decay model ... more

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; The initial temperature of water is and the ... more

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, basic ; Evaluate the expression at . Since , ... more

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; Evaluate the equation at . ; Evaluate the ... more

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; The pH of a substance is given by the equation... more

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; Use the formula of the magnitude of an ... more

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About 2512 times ; Find the intensity, , of an ... more

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About 6 times ; Find the intensity, , of an ... more

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About 2.5 times ; Find the intensity, , of an ... more

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73 dB ; Substitute and in the formula of decibel... more

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105 dB ; Substitute and in the formula of ... more

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  ; Substitute and in the formula of decibel ... more

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; Substitute and in the formula of decibel ... more

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; Let and be the decibel level and intensity of... more

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The function increases more rapidly than . ; ... more

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 Where , , , and are real numbers, , , , and . ; ... more

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; Express the formula for . The constant is ... more

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0.0899.73955.902 ; Substitute for into . ... more

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0.65318.775135.765 ; Substitute for into . ... more

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; Solve for .Substitute for in .Evaluate using ... more

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; Solve for .Substitute for in .Evaluate using ... more

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; Create a table of values for and .Choose ... more

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; Create a table of values for and .Choose ... more

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; Create a table of values for and .Choose ... more

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; Create a table of values for and .Choose ... more

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; Create a table of values for and .Choose ... more

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; Create a table of values for and .Choose ... more

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; Create a table of values for and .Choose ... more

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; Create a table of values for and .Choose ... more

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; Create a table of values for and .Choose ... more

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; Create a table of values for and .Choose ... more

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; Create a table of values for and .Choose ... more

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; Create a table of values for and .Choose ... more

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; The given function is the sum of the ... more

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; The argument of the logarithm must be positive ... more

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; The argument of the logarithm must be positive ... more

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; The argument of the logarithm must be positive ... more

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; Use the property to rewrite the given equation... more

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; Use the property to rewrite the given equation... more

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; Use the property to rewrite the given equation... more

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; Use the property to rewrite the given equation... more

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; Use the property to rewrite the given equation... more

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; Use the property to rewrite the given equation... more

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; Use the property to rewrite the given equation... more

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; Use the property to rewrite the given equation... more

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7 ; Write 128 as .Apply the power rule to bring ... more

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0 ; Write 1 as .Use the power rule of logarithm ... more

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45 ; Use the property to find the value of the ... more

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; Write as .Use the power rule to bring down ... more

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6 ; Use the power rule to bring down the exponent... more

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; Write 8 as .Write as .Write as .Use the power... more

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; Write as .Write 27 as .Use the power rule of ... more

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13 ; Use the property to find the value of the ... more

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; Write as .Use the power rule of logarithm to ... more

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49 ; Use the power rule of logarithm to bring ... more

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2 ; Condense the logarithm using the product rule... more

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; Write as .Write as .Apply the power rule of ... more

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92 ; Write 16 as .Use the power rule of exponents... more

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3 ; Condense the logarithm using the quotient rule... more

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; Rewrite the given expression into one ... more

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2 ; Use the power rule to bring down the exponent... more

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; Expand the given logarithm.Use the product rule... more

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; Rewrite the given logarithm.Use the product ... more

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; Use the quotient rule to write the given ... more

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; Use the quotient rule to write the given ... more

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; Let the given expression be . Use the quotient ... more

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; Let the given expression be . Use the quotient ... more

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; Use the power rule to rewrite the second term... more

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; Use the power rule   to rewrite the third ... more

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; Rewrite each term using the law .Write as the ... more

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; Use the law in the last term to write as the ... more

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; Use the law in the last term to write as the ... more

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; Distribute to each term inside the brackets... more

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5 ; Write 27 as so that the exponential ... more

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7 ; Write 125 in the given right-hand side as . ; ... more

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; Take the of both sides of the given equation.... more

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; Take the of both sides of the given equation.... more

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; Take the of both sides of the given equation. ... more

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; Take the of both sides of the given equation. ... more

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, 2 ; Subtract from both sides of the given ... more

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1 ; Express the given equation into a quadratic ... more

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3 ; Use the property to combine the logarithm ... more

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No solution ; Use the property to combine the ... more

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; Write the given logarithmic equation into its ... more

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; Subtract 1 from both sides of the given ... more

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9 ; Use the property to combine the logarithm ... more

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3 ; Use the property to combine the logarithmic ... more

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0.430618 ; Take the of both sides of the given ... more

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2.602452 ; Take the of both sides of the given ... more

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2.303600 ; Take the of both sides of the given ... more

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; Take the of both sides of the given equation.... more

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Vertical asymptote: Horizontal asymptote: No ... more

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Horizontal asymptote: Local minimum: ; Graph the ... more

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Vertical asymptotes: , , and Local maximum: ; ... more

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Vertical asymptote:  Local minimum: No maximum ; ... more

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2.42 ; Enter and into a graphing utility and use... more

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, ; Enter and into a graphing utility and use ... more

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; Enter and into a graphing utility and adjust ... more

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or ; Subtract from both sides of the given ... more

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Increasing on and Decreasing on ; Graph the given... more

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; Find the coordinates of the point of ... more

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1.953445 ; Convert the given logarithm into a ... more

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; Convert the given logarithm into a common ... more

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; Convert the given logarithm into a common ... more

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1.198970 ; Convert the given logarithm into a ... more

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; Convert into a common logarithm:Use the ... more

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Domain of : Range of : ; Write and interchange ... more

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1.83 years ; Write the amount , as the sum of the ... more

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15.40 years ; Use the formula for continuous ... more

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; The annual percentage yield, APY, is the ... more

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; The annual percentage yield, APY, is the ... more

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43 minutes ; Let be the initial difference in the... more

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7.9, basic ; Evaluate the expression at the given... more

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M ; The pH of a substance is given by the ... more

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8.0 ; Find the intensity of the earthquake with ... more

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; Find the intensity of the sound with decibel ... more

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1.326 ; Use the formula to change the base of the... more

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1995 times more intense ; Find the intensity, , of... more

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, where and ; Enter the data into a graphing ... more

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