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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