How can we prove this?

Question

Hello! When I was practicing math I stumbled upon on a problem:

prove, xloga(y) = yloga(x)

I couldn't solve it. I hope you can solve it. Thanks in advance.

Answer 1

Moshiur,

as written, it is a typographical error, therefore false.

It should have been

x^(log_a(y)) = y^(log_a(x))

Hint: take the log_a of both sides, remembering that

log(x^y) = ylog(x)

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