Given that \(\log_{2} y^{\frac{1}{2}} = \log_{5} 125\), find the value of y.
FURTHER MATHEMATICS
WAEC 2007
Given that \(\log_{2} y^{\frac{1}{2}} = \log_{5} 125\), find the value of y.
- A. 16
- B. 25
- C. 36
- D. 64
Correct Answer: D. 64
Explanation
\(\log_{2} y^{\frac{1}{2}} = \log_{5} 125\)
\(\log_{2} y^{\frac{1}{2}} = \log_{5} 5^{3} = 3\log_{5} 5 = 3\)
\(\log_{2} y^{\frac{1}{2}} = 3 \implies y^{\frac{1}{2}} = 2^{3} = 8\)
\(y = 8^{2} = 64\)
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