If \(\sqrt{3^{\frac{1}{x}}}\) = \(\sqrt{9}\) then the value of x is:
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Correct Answer: Option E
Explanation:
\(\sqrt{3^{\frac{1}{x}}}\) = \(\sqrt{9}\)
3\(^{\frac{1}{2x}}\) = \(9^{\frac{1}{2}}\)
3\(^{\frac{1}{2x}}\) = 3\(^{2 \times \frac{1}{2}}\)
3\(\frac{1}{2x}\) = 3\(\frac{2}{2}\) = 3
\(3^{\frac{1}{2x}}\) = \(3^{1}\)
\(\frac{1}{2x}\) = \(\frac{1}{1}\)
x = \(\frac{1}{2}\)
\(\sqrt{3^{\frac{1}{x}}}\) = \(\sqrt{9}\)
3\(^{\frac{1}{2x}}\) = \(9^{\frac{1}{2}}\)
3\(^{\frac{1}{2x}}\) = 3\(^{2 \times \frac{1}{2}}\)
3\(\frac{1}{2x}\) = 3\(\frac{2}{2}\) = 3
\(3^{\frac{1}{2x}}\) = \(3^{1}\)
\(\frac{1}{2x}\) = \(\frac{1}{1}\)
x = \(\frac{1}{2}\)