Evaluate \(\log_{b} a^{n}\) if \(b = a^{\frac{1}{n}}\).
A
n2
B
n
C
\(\frac{1}{n}\)
D
\(\frac{1}{n^2}\)
Verified Correct Answer: A.
Step-by-Step Mathematical Solution
Let \(\log_{b} a^{n} = x\)
\(\therefore a^{n} = b^{x}\)
\(a^{n} = (a^{\frac{1}{n}})^{x}\)
\(a^{n} = a^{\frac{x}{n}} \implies n = \frac{x}{n}\)
\(x = n^{2}\)
Source: Myschool Past Questions Archive (Record #31293)