Chapter 4, Exponential and Logarithmic Functions - Section 4.4 - Laws of Logarithms - 4.4 Exercises - Page 396: 77

First line is wrong.

This statement on the first line is wrong: $\log 0.1<2\log 0.1$ This is because $\log 0.1$ is negative (it equals $-1$). A negative number multiplied by $2$ becomes a larger negative number. So in fact: $2\log 0.1\lt \log 0.1$