Chapter 12 - Exponential Functions and Logarithmic Functions - 12.5 Common Logarithms and Natural Logarithms - 12.5 Exercise Set - Page 818: 43

$-3.3219$

Using $\log_b a=\dfrac{\log a}{\log b}$ or the Change-of-Base Formula, the value of the given expression, $ \log_{2} 0.1 ,$ to four decimal places is \begin{array}{l}\require{cancel} \dfrac{\log 0.1}{\log 2} \\\\= -3.3219 .\end{array}