If \(\log_{3} x = \log_{9} 3\), find the value of x.
FURTHER MATHEMATICS
WAEC 2015
If \(\log_{3} x = \log_{9} 3\), find the value of x.
- A. \(3^{2}\)
- B. \(3^{\frac{1}{2}}\)
- C. \(3^{\frac{1}{3}}\)
- D. \(2^{13}\)
Correct Answer: B. \(3^{\frac{1}{2}}\)
Explanation
\(\log_{3} x = \log_{9} 3 \implies \log_{3} x = \log_{9} 9^{\frac{1}{2}} = \frac{1}{2}\log_{9} 9\)
\(\log_{3} x = \frac{1}{2} \)
\(\therefore x = 3^{\frac{1}{2}}\)
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