Intermediate Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-894-7
ISBN 13: 978-0-13417-894-3

Chapter 9 - Section 9.4 - Properties of Logarithms - Exercise Set - Page 714: 119

Answer

See explanation

Work Step by Step

The change of base property states that: for any logarithm base $a$ and $b$ and any positive number M, $\log_{b}M=\frac{\log_{a}M}{ \log_{a}b}$ The logarithm of $M$ with base $b$ is equal to the logarithms of $M$ with any new base divided by the logarithm of $b$ with that new base, Therefore, $$\log e=\frac{\log_{e} e}{\log_{e}10}=\frac{1}{\ln 10}$$
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