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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