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

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

A.

1/6

B.

3/8

C.

1/2

D.

3/4

E.

6

View answer & explanation

Correct answer is B

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

= $\frac{\log \sqrt{3^3}}{\log 3^4}$

= $\frac{\log 3^{\frac{3}{2}}}{\log 3^4}$

= $\frac{\frac{3}{2} \log 3}{4 \log 3}$

= $\frac{\frac{3}{2}}{4}$

= $\frac{3}{8}$

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