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Simplify $\frac{\log \sqrt{27}}{\log \sqrt{81}}$ ...

Simplify $\frac{\log \sqrt{27}}{\log \sqrt{81}}$

A.

3

B.

2

C.

$\frac{3}{2}$

D.

$\frac{3}{4}$

View answer & explanation

Correct answer is D

$\frac{\log \sqrt{27}}{\log \sqrt{81}}$ = $\frac{\log 27\frac{1}{2}}{81\frac{1}{2}}$

= $\frac{\log 3\frac{1}{2}}{\log 3^2}$

$\frac{\frac{3}{2} \log 3}{2 \log 3} = \frac{3}{2} \div \frac{2}{1}$

= $\frac{3}{2} \times \frac{1}{2}$

= $\frac{3}{4}$

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