Is a^(ln b) = b^(ln a)? 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

Celia Ray

Celia Ray

Answered question

2022-11-27

Is a ln b = b ln a ?
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?

Answer & Explanation

Nicholas Lara

Nicholas Lara

Beginner2022-11-28Added 10 answers

Do this:
a ln ( b ) = e ln ( a ) ln ( b ) = b ln ( a ) .

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