Home » If (sqrt{3^{frac{1}{x}}}) = (sqrt{9}) then the value of x is:

If (sqrt{3^{frac{1}{x}}}) = (sqrt{9}) then the value of x is:

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})
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})