Question 8

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Jambmaths question: 

If ${{\log }_{{{x}^{\tfrac{1}{2}}}}}64=3$, find the value of x

Option A: 

4

Option B: 

16

Option C: 

32

Option D: 

64

Jamb Maths Solution: 

$\begin{align}  & {{\log }_{{{x}^{\tfrac{1}{2}}}}}64=3 \\ & \text{Note: }{{\log }_{{{a}^{n}}}}b=\frac{1}{n}{{\log }_{a}}b \\ & \therefore {{\log }_{{{x}^{\tfrac{1}{2}}}}}64=\frac{1}{\tfrac{1}{2}}{{\log }_{x}}64=3 \\ & 2{{\log }_{x}}64=3 \\ & {{\log }_{x}}64=\frac{3}{2},{{x}^{\tfrac{3}{2}}}=64 \\ & x=\sqrt[3]{{{64}^{2}}}=\sqrt[3]{4096}=16 \\\end{align}$

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