Competition problem — Algebra — Maths Olympiad Prep

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Algebra Difficulty 5.2 AIME, harder Prove it

1. Let $00, a \neq 1$ , prove: $\left|\log _{a}(1-x)\right|>\left|\log _{a}(1+x)\right|$ .

Solution

1. Prompt: Use the comparison method.

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Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.