Jambmaths question:
Evaluate ${{5}^{-3{{\log }_{5}}2}}\times {{2}^{2{{\log }_{2}}3}}$
Option A:
8
Option B:
$1\tfrac{1}{8}$
Option C:
$\tfrac{2}{5}$
Option D:
$\tfrac{1}{8}$
Jamb Maths Solution:
$\begin{align} & \text{Note: }{{m}^{x{{\log }_{m}}y}}={{y}^{x}} \\ & {{5}^{-3{{\log }_{5}}2}}={{2}^{-3}}\text{=}\frac{1}{8}\text{ }\!\!\{\!\!\text{ }{{m}^{x{{\log }_{m}}y}}={{y}^{x}}\} \\ & {{2}^{2{{\log }_{2}}3}}={{3}^{2}}=9\text{ }\!\!\{\!\!\text{ }{{m}^{x{{\log }_{m}}y}}={{y}^{x}}\} \\ & \therefore {{5}^{-3{{\log }_{5}}2}}\times {{2}^{2{{\log }_{2}}3}}=\frac{1}{8}\times 9=\frac{9}{8}=1\frac{1}{8} \\\end{align}$
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