How to calculate this limit? $$\lim\limits_{n \to \infty} \frac{\log(1+2^n)}{\log(1+3^n)}$$
2026-05-14 20:11:25.1778789485
Find $\lim\limits_{n \to \infty} \frac{\log(1+2^n)}{\log(1+3^n)}$
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Using continuity (fill in details):
$$\frac{\log(1+2^n)}{\log(1+3^n)}=\frac{n\log 2+\log\left(1+\frac1{2^n}\right)}{n\log 3+\log\left(1+\frac1{3^n}\right)}\xrightarrow[n\to\infty]{}\frac{\log2}{\log3}$$