Logarithmic inequality for powers

Prove that $\frac{1}{m} lo g (1 + a^{m}) < \frac{1}{n} lo g (1 + a^{n})$ , if $m > n$ .

~10 minProof · checked by AIInequalitiesLogarithmsCalculus

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. XIX. Inequalities, Examples XIX.b, No. 7

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