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3.3 The logarithm as an inverse function

The logarithm as an inverse functionIn this section we concentrate onunderstandingthe logarithm function . If the logarithm is understoodas the inverse of the exponential function , then the variety of properties of logarithms will be seen asnaturally flowing out of our rules for The meaning of the logarithmThe logarithmic functiong(x) = logb(x) is the inverse of an exponential functionf(x) = so themeaningofy= logb(x) isby= expressionby=xis said to be the exponential form for thelogarithmy= logb(x). The positive constantbis called thebase(of the logarithm .)Some worked each of the following logarithms in exponential form and then use that exponential form tosolve log2(8) = exponential form is 2x= 23= 8 the answer isx= log2(247) = exponential form is 2x= log2(12) = exponential form is 2x= 2 1=12the answer isx= log2(18) = exponential form is 2x= 2 3=18the answer isx= log2(3 2) = exponential form is 2x= 21 1 The graph of a logarithm functionThe graph ofy= 2xwas drawn in an earlier lecture (see figure 1.)

3.3.6Other resources for logarithmic functions In the free textbook, Precalculus, by Stitz and Zeager (version 3, July 2011, available atstitz-zeager.com) this material is covered in sections 6.2 and 6.3. In the free textbook, Precalculus, An Investigation of Functions, by Lippman and Rassmussen (Edition

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