Question

The value of ${\log }_{\frac{2}{3}}\frac{5}{6}$ is

• A. less than zero.
• B. greater than zero and less than one.
• C. greater than one.
• D. none of these

Answer 1

The correct option is B greater than zero and less than one.

$\frac{2}{3}<\frac{5}{6}<1$
Taking log with base $\frac{2}{3}$
${\log }_{\frac{2}{3}}\frac{2}{3}>{\log }_{\frac{2}{3}}\frac{5}{6}>{\log }_{\frac{2}{3}}1$ (Since the base $\frac{2}{3}<1)$
$\Rightarrow 1>{\log }_{\frac{2}{3}}\frac{5}{6}>0$