JAMB - Mathematics (1992 - No. 3)
Evaluate \(\log_{b} a^{n}\) if \(b = a^{\frac{1}{n}}\).
n2
n
\(\frac{1}{n}\)
\(\frac{1}{n^2}\)
Explicación
Let \(\log_{b} a^{n} = x\)
\(\therefore a^{n} = b^{x}\)
\(a^{n} = (a^{\frac{1}{n}})^{x}\)
\(a^{n} = a^{\frac{x}{n}} \implies n = \frac{x}{n}\)
\(x = n^{2}\)