College Algebra (6th Edition)

Published by Pearson
ISBN 10: 0-32178-228-3
ISBN 13: 978-0-32178-228-1

Chapter 4 - Exponential and Logarithmic Functions - Exercise Set 4.2 - Page 467: 123

Answer

" The logarithm of a power of the base is the exponent of that power"

Work Step by Step

$b^{x}$ is a power of b, with exponent x. so the formula can be read as " The logarithm of a power of the base is the exponent of that power" This stems from the definition (see p.456) The logarithm of $b^{x}$ with base b is a number y, $y=\log_{b}b^{x}$, such that $b^{y}=b^{x}.$ So, by the basic property of exponential functions, $y=x,$ $\log_{b}b^{x}=x$
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