Evaluate (log_{b} a^{n}) if (b = a^{frac{1}{n}}).
-
A.
n2 -
B.
n -
C.
(frac{1}{n}) -
D.
(frac{1}{n^2})
Correct Answer: Option A
Explanation
Let (log_{b} a^{n} = x)
(therefore a^{n} = b^{x})
(a^{n} = (a^{frac{1}{n}})^{x})
(a^{n} = a^{frac{x}{n}} implies n = frac{x}{n})
(x = n^{2})