Simplify (frac{log sqrt{27}}{log sqrt{81}})
-
A.
3 -
B.
2 -
C.
(frac{3}{2}) -
D.
(frac{3}{4})
Correct Answer: Option D
Explanation
(frac{log sqrt{27}}{log sqrt{81}}) = (frac{log 27frac{1}{2}}{81frac{1}{2}})
= (frac{log 3frac{1}{2}}{log 3^2})
(frac{frac{3}{2} log 3}{2 log 3} = frac{3}{2} div frac{2}{1})
= (frac{3}{2} times frac{1}{2})
= (frac{3}{4})