Question

What is the value of $lo{g}_{\frac{1}{3}}9\sqrt{3}$

• A. $\frac{2}{5}$
• B. $\frac{5}{2}$
• C. $\frac{-2}{5}$
• D. $\frac{-5}{2}$

Answer 1

The correct option is D

$\frac{-5}{2}$

Let $lo{g}_{\frac{1}{3}}9\sqrt{3}=x$

$\Rightarrow 9\sqrt{3}=(\frac{1}{3}{)}^x$

$\Rightarrow 3^2\times 3^{\frac{1}{2}}=3^{-x}$

$\Rightarrow 3^{\frac{5}{2}}=3^{-x}$

$\Rightarrow x=\frac{-5}{2}$