Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 12 - Exponential Functions and Logarithmic Functions - 12.5 Common Logarithms and Natural Logarithms - 12.5 Exercise Set - Page 819: 88

Answer

Sample answer: $\ln M=\ln 10\cdot\log M$ $ ($if we know $\log M$, mulitply with $\ln 10$ to obtain $\ln M$)

Work Step by Step

Common logarithms: Instead of $\log_{10}x$, we write $\log x.$ natural logarithm: For base $ e\approx 2.7182818284$, we write $\ln x$ instead of $\log_{e}x.$ Using change-of-base, $\displaystyle \log_{b}M=\frac{\log_{a}M}{\log_{a}b}$, we change base 10 to $e$ $\displaystyle \log M=\frac{\ln M}{\ln 10}$ $\ln M=\ln 10\cdot\log M$ $ ($if we know $\log M$, mulitply with $\ln 10$ to obtain $\ln M$)
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