Evaluate \(\log_{b} a^{n}\) if \(b = a^{\frac{1}{n}}\).
Take Free Practice Test On 2026 JAMB UTME, Post UTME, WAEC SSCE, GCE, NECO SSCE
Correct Answer: Option A
Explanation:
Let \(\log_{b} a^{n} = x\)
\(\therefore a^{n} = b^{x}\)
\(a^{n} = (a^{\frac{1}{n}})^{x}\)
\(a^{n} = a^{\frac{x}{n}} \implies n = \frac{x}{n}\)
\(x = n^{2}\)
Let \(\log_{b} a^{n} = x\)
\(\therefore a^{n} = b^{x}\)
\(a^{n} = (a^{\frac{1}{n}})^{x}\)
\(a^{n} = a^{\frac{x}{n}} \implies n = \frac{x}{n}\)
\(x = n^{2}\)