waecmaths question:
If ${{(0.25)}^{y}}=32$ . Find the value of y
Option A:
$y=-\frac{5}{2}$
Option B:
$y=-\frac{3}{2}$
Option C:
$y=\frac{3}{2}$
Option D:
$y=\frac{5}{2}$
waecmaths solution:
$\begin{align} & {{(0.25)}^{y}}=32 \\ & {{\left( \frac{25}{100} \right)}^{y}}={{2}^{5}} \\ & {{\left( \frac{1}{4} \right)}^{y}}={{2}^{5}} \\ & {{({{4}^{-1}})}^{y}}={{2}^{5}} \\ & {{({{2}^{2}})}^{-y}}={{2}^{5}} \\ & {{2}^{-2y}}={{2}^{5}} \\ & \text{Equating the powers} \\ & -2y=5 \\ & y=-\frac{5}{2} \\\end{align}$
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