Question

The value of $lo{g}_{0.008}\sqrt{5}+lo{g}_{\sqrt{3}}81-7$ is equal to

• A. $\frac{1}{3}$
• B. $\frac{2}{3}$
• C. $\frac{5}{6}$
• D. $\frac{7}{6}$

Answer 1

The correct option is C

$\frac{5}{6}$

$lo{g}_{0.008}\sqrt{5}+lo{g}_{\sqrt{3}}81-7\Rightarrow lo{g}_{{\left(\frac{1}{5}\right)}^3}{5}^{\frac{1}{2}}+2\times lo{g}_3{3}^4-7\Rightarrow \frac{\left(\frac{1}{6}\right)}{lo{g}_5\left(\frac{1}{5}\right)}+8-7\Rightarrow 1-\frac{1}{6}=\frac{5}{6}$