Chapter 4 - Inverse, Exponential, and Logarithmic Functions - 4.4 Evaluation Logarithms and the Change-of-Base Theorem - 4.4 Exercises - Page 456: 13

$-1$

Apply logarithmic property : $\log a^ b=b \log a$ Re-write as: $\log 0.1=\log \dfrac{1}{10}=\log 10^{-1}$ $\log (10)^{-1}=-1 \log (10)$ Now, take logarithmic to the base $10$ and evaluate the result. Therefore, our answer is: $\log (10)^{-1}=-1 \log_{10} (10)=-1$