Chapter 12 - Exponential Functions and Logarithmic Functions - 12.5 Common Logarithms and Natural Logarithms - 12.5 Exercise Set - Page 819: 89

Sample answer: $\displaystyle \log M=\frac{\ln M}{\ln 10}$ $ ($if we know $\ln M$, divide it with $\ln 10$ to obtain $\log M$)

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 $e$ $\displaystyle \log M=\frac{\ln M}{\ln 10}$ $ ($if we know $\ln M$, divide it with $\ln 10$ to obtain $\log M$)