If \(\sqrt{3^{\frac{1}{x}}}\) = \(\sqrt{9}\) then the value of x is:
- \(\frac{3}{4}\)
- \(\frac{4}{3}\)
- \(\frac{1}{3}\)
- \(\frac{2}{3}\)
-
\(\frac{1}{2}\)
The correct answer is: 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 = \(\frac{1}{2}\)