Part of ALG-11 — Logarithms, Exponentials & Functional Equations

Exponential Growth and Comparison

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For large x: exponential growth dominates polynomial growth. That is, axa^x grows faster than xnx^n for any fixed n when a > 1. Conversely, log functions grow slower than any positive power: log(x) < xepsilonx^{epsilon} for large x. In JEE, this helps in comparing terms and finding limits. Also: among exponentials, the one with the larger base dominates (3^x >> 2^x for large x).

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