Chapter 12 - Exponential Functions and Logarithmic Functions - 12.5 Common Logarithms and Natural Logarithms - 12.5 Exercise Set - Page 818: 41

$-0.3010$

Applying $\displaystyle \log_{b}M=\frac{\log_{a}M}{\log_{a}b}$, $\displaystyle \log_{0.1}2=\frac{\log_{10}2}{\log_{10}0.1}$ $=\displaystyle \frac{\log_{10}2}{\log_{10}10^{-1}}=\frac{\log 2}{-1}\approx-0.301029995664$ To four decimal places, $-0.3010$