Question 4

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waecmaths question: 

If $\frac{{{27}^{x}}\times {{3}^{1-x}}}{{{9}^{2x}}}=1$, find the value of x

Option A: 

1

Option B: 

$-\tfrac{1}{2}$

Option C: 

$-\tfrac{1}{2}$

Option D: 

–1

waecmaths solution: 

$\begin{align}  & \frac{{{27}^{x}}\times {{3}^{1-x}}}{{{9}^{2x}}}=1 \\ & \frac{{{3}^{3x}}\times {{3}^{1-x}}}{{{3}^{2(2x)}}}=1 \\ & {{3}^{3x+1-x-4x}}=1 \\ & {{3}^{-2x+1}}={{3}^{0}} \\ & \text{Equating the powers, since the base are equal} \\ & -2x+1=0 \\ & x=-\frac{1}{2} \\\end{align}$

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