If \(\log_{9} 3 + 2x = 1\), find x.
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Correct Answer: Option C
Explanation:
\(\log_{9} 3 = \log_{9} (9^{\frac{1}{2}}) = \frac{1}{2}\log_{9} 9 = \frac{1}{2}\)
\(\frac{1}{2} + 2x = 1 \implies 2x = \frac{1}{2}\)
\(x = \frac{1}{4}\)
\(\log_{9} 3 = \log_{9} (9^{\frac{1}{2}}) = \frac{1}{2}\log_{9} 9 = \frac{1}{2}\)
\(\frac{1}{2} + 2x = 1 \implies 2x = \frac{1}{2}\)
\(x = \frac{1}{4}\)