Exponential and logarithmic inequalities

If $a > b$ , show that $a^{a} b^{b} > a^{b} b^{a}$ , and $lo g \frac{b}{a} < lo g \frac{1 + b}{1 + a}$ .

~8 minProof · checked by AIInequalitiesLogarithmsExponentials

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. XIX. Inequalities, Examples XIX.a, No. 6

Stuck? A gentle nudge

Something off?

Workspace

Your working

Check your full solution

Upload photos of your handwritten work or a PDF, and Lemma will read it and tell you whether it's right — and where it first goes wrong if not.