Question 17

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waecmaths question: 

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

Option A: 

3

Option B: 

2

Option C: 

$\tfrac{3}{2}$

Option D: 

$\tfrac{3}{4}$

waecmaths solution: 

$\begin{align}  & \frac{\log \sqrt{27}}{\log \sqrt{81}}=\frac{\log {{27}^{\tfrac{1}{2}}}}{\log {{81}^{\tfrac{1}{2}}}} \\ & =\frac{\log {{({{3}^{3}})}^{\tfrac{1}{2}}}}{\log {{({{3}^{4}})}^{\tfrac{1}{2}}}}=\frac{\log {{3}^{\tfrac{3}{2}}}}{\log {{3}^{\tfrac{4}{2}}}} \\ & =\frac{\tfrac{3}{2}\log 3}{\tfrac{4}{2}\log 3}=\frac{\tfrac{3}{2}}{2}=\frac{3}{4} \end{align}$

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