1. Objective: To graph logarithmic functions, to convert between exponential and logarithmic equations, and find common and natural logarithms using a calculator.

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12.  Since exponential and logarithmic functions are inverses of each other, their graphs are also inverses.  Logarithmic function and exponential function are inverses of each other.  The domain of the exponential function is all reals, so that’s the domain of the logarithmic function.  The range of the exponential function is x>0, so the range of the logarithmic function is y>0.

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14. (  3,1/27) 1/27 33 (  2, 1/9) 1/9 22 (  1, 1/3) 1/3 11 (3, 27)273 9 3 1 y = f(x) = 3 x (2, 9)2 (1, 3)1 (0, 1)0 (x, y)x

15. f(x)= 3 x (0, 1) (1, 3) (2, 9) (3, 27) (  1, 1/3) (  2, 1/9) (  3,1/27)

16.  See Table 3.4 on Transformations.

17.  Logarithmic functions are inverses of exponential functions.  Easier if rewrite as an exponential before graphing. 1.Choose values for y. 2.Compute values for x. 3.Plot the points and connect them with a smooth curve. * Note that the curve does not touch or cross the y-axis.

19.  Since a positive number raised to an exponent (pos. or neg.) always results in a positive value, you can ONLY take the logarithm of a POSITIVE NUMBER.  Remember, the question is: What POWER can I raise the base to, to get this value?  DOMAIN RESTRICTION:

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21.  If no value is stated for the base, it is assumed to be base 10.  log(1000) means, “What power do I raise 10 to, to get 1000?” The answer is 3.  log(1/10) means, “What power do I raise 10 to, to get 1/10?” The answer is -1.

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23.  Round to four decimal places. a) log 723,456 b) log 0.0000245 c) log (  4) Common LogReadoutRounded

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25.  * ln button on your calculator is the natural log *

26.  Round to four decimal places. a) ln 723,456 b) ln 0.0000245 c) ln (  4) Natural LogRead outRounded