Question 31

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waecmaths question: 

If ${{\log }_{a}}270-{{\log }_{a}}10+{{\log }_{a}}\tfrac{1}{3}=2$ what is the value of a?

Option A: 

3

Option B: 

4

Option C: 

5

Option D: 

6

waecmaths solution: 

$\begin{align}  & {{\log }_{a}}270-{{\log }_{a}}10+{{\log }_{a}}\tfrac{1}{3}=2 \\ & {{\log }_{a}}\frac{270\times \tfrac{1}{3}}{10}=2 \\ & {{\log }_{a}}9=2 \\ & {{a}^{2}}=9 \\ & {{a}^{2}}={{3}^{2}} \\ & a=3 \\\end{align}$

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