Question 31

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waecmaths question: 

If ${{9}^{2x}}=\tfrac{1}{3}({{27}^{x}})$ find x

Option A: 

2

Option B: 

1

Option C: 

–1

Option D: 

–2

waecmaths solution: 

$\begin{align}  & {{9}^{2x}}=\tfrac{1}{3}({{27}^{x}}) \\ & {{3}^{2(2x)}}=\tfrac{1}{3}({{3}^{3x}}) \\ & {{3}^{4x}}={{3}^{-1}}({{3}^{3x}}) \\ & {{3}^{4x}}={{3}^{-1+3x}} \\ & \text{Equating the powers} \\ & 4x=-1+3x \\ & x=1 \\\end{align}$

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