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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. \(\frac{1}{2}\)
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Correct Answer: Option C
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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