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 4.3 - Page 477: 101



Work Step by Step

Using the Change-of-Base Property, $\displaystyle \log_{b}M=\frac{\log_{a}M}{\log_{a}b}$, we want to change the base of the logarithm on the LHS from 3 to 7: b=3, M=7, a=7: $LHS=\displaystyle \log_{3}7=\frac{\log_{7}7}{\log_{7}3}$ = ... ... the numerator equals 1, by the basic property $\log_{b}b=1$, $=\displaystyle \frac{1}{\log_{7}3}=RHS,$ so the problem statement is true.
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