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Unformatted text preview: eneralize out to log b b f ( x ) = f ( x ) . 4. blogb x = x . This can be generalize out to blogb f ( x ) = f ( x ) . © 2007 Paul Dawkins 289 http://tutorial.math.lamar.edu/terms.aspx College Algebra Properties 3 and 4 leads to a nice relationship between the logarithm and exponential function.
Let’s first compute the following function compositions for f ( x ) = b x and g ( x ) = log b x . ( f o g ) ( x ) = f é g ( x )ù = f ( logb x ) = blog x = x
( g o f )( x ) = g é f ( x )ù = g éb x ù = log b b x = x
b Recall from the section on inverse functions that this means that the exponential and logarithm
functions are inverses of each other. This is a nice fact to remember on occasion.
We should also give the generalized version of Properties 3 and 4 in terms of both the natural
and common logarithm as we’ll be seeing those in the next couple of sections on occasion. ln e f ( x ) = f ( x ) e ln f ( x ) log10 f ( x ) = f ( x ) = f ( x) 10log f ( x ) = f ( x ) Now, let’s take a look at some manipulation properties of the logarithm.
More Properties of Logarithms
For these properties w...
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- Spring '12