Transcription of 3.3 The logarithm as an inverse function
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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
3.3.3 Properties of exponential functions in terms of logarithms The logarithm function plucks the exponent from an expression. For this reason, the properties of exponents translate into properties of logarithms. For example, we know that when we multiply two terms with a common base, we add the exponents: (bx)(by) = bx+y (8)
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