If \(\sqrt{3^{\frac{1}{x}}}\) = \(\sqrt{9}\) then the value of x is:
A
\(\frac{3}{4}\)
B
\(\frac{4}{3}\)
C
\(\frac{1}{3}\)
D
\(\frac{2}{3}\)
E
\(\frac{1}{2}\)
Verified Correct Answer: E.
Step-by-Step Mathematical Solution
\(\sqrt{3^{\frac{1}{x}}}\) = \(\sqrt{9}\)
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 = \(\frac{1}{2}\)
Source: Myschool Past Questions Archive (Record #32683)