Mathematics

Simplify: (frac{log sqrt{27}}{log sqrt{81}})

Simplify: (frac{log sqrt{27}}{log sqrt{81}})

  • A.
    1/6
  • B.
    3/8
  • C.
    1/2
  • D.
    3/4
  • E.
    6
Correct Answer: Option B
Explanation

(frac{log sqrt{27}}{log 81})

= (frac{log sqrt{3^3}}{log 3^4})

= (frac{log 3^{frac{3}{2}}}{log 3^4})

= (frac{frac{3}{2} log 3}{4 log 3})

= (frac{frac{3}{2}}{4})

= (frac{3}{8})