If \(\log_{9} 3 + 2x = 1\), find x.
FURTHER MATHEMATICS
WAEC 2011
If \(\log_{9} 3 + 2x = 1\), find x.
- A. \(\frac{-1}{2}\)
- B. \(\frac{-1}{4}\)
- C. \(\frac{1}{4}\)
- D. \(\frac{1}{2}\)
Correct Answer: C. \(\frac{1}{4}\)
Explanation
\(\log_{9} 3 = \log_{9} (9^{\frac{1}{2}}) = \frac{1}{2}\log_{9} 9 = \frac{1}{2}\)
\(\frac{1}{2} + 2x = 1 \implies 2x = \frac{1}{2}\)
\(x = \frac{1}{4}\)
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