Question 8

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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: 

${{m}^{x{{\log }_{m}}y}}={{y}^{x}}$The proof of this is beyond the scope of this book for now. Just accept this knowledge,$\begin{align}  & {{5}^{-3{{\log }_{5}}2}}={{2}^{-3}}\text{=}\frac{1}{8}\text{               }\!\!\{\!\!\text{ }{{m}^{x{{\log }_{m}}y}}={{y}^{x}}\} \\ & {{2}^{2{{\log }_{2}}3}}={{3}^{2}}=9\text{          }\!\!\{\!\!\text{ }{{m}^{x{{\log }_{m}}y}}={{y}^{x}}\} \\ & \therefore {{5}^{-3{{\log }_{5}}2}}\times {{2}^{2{{\log }_{2}}3}}=\frac{1}{8}\times 9=\frac{9}{8}=1\frac{1}{8} \\\end{align}$

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