Chapter 1.8, Problem 47ES

Find the fallacy in the following “proof� that $\frac{1}{8}>\frac{1}{4}$ . Multiply both sides of the inequality $3>2$ by $\log \frac{1}{2}$ to get

$3\log \frac{1}{2}>2\log \frac{1}{2}$

$\log {\left(\frac{1}{2}\right)}^3>\log {\left(\frac{1}{2}\right)}^2$

$\log \frac{1}{8}>\log \frac{1}{4}$

$\frac{1}{8}>\frac{1}{4}$