I was struggling with a math problem, namely, a limit with a power to the log of something. While I was struggling with it, I found out that $$a^{\ln b} = b^{\ln a}$$ for all positive values that I've tested. Is it true? And if so, can you provide a proof?
2026-04-09 11:01:19.1775732479
Is $a^{\ln b} = b^{\ln a}$?
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Do this:
$$a^{\ln(b)} = e^{\ln(a)\ln(b)} = b^{\ln(a)}.$$