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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