Simplify \(\frac{\log_{5} 8}{\log_{5} \sqrt{8}}\).
FURTHER MATHEMATICS
WAEC 2010
Simplify \(\frac{\log_{5} 8}{\log_{5} \sqrt{8}}\).
- A. -2
- B. \(\frac{-1}{2}\)
- C. \(\frac{1}{2}\)
- D. 2
Correct Answer: D. 2
Explanation
\(\frac{\log_{5} 8}{\log_{5} \sqrt{8}} = \frac{\log_{5} 8}{\log_{5} 8^{\frac{1}{2}}}\)
= \(\frac{\log_{5} 8}{\frac{1}{2}\log_{5} 8}\)
= \(\frac{1}{\frac{1}{2}} \)
= 2
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