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Logs in the exponent

Guest jmcgigge
Guest jmcgigge
in Analysis and Calculus

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I'm trying to find a proof for the following equation:

 

x*y^ln(x)=x^ln(y)+1

 

It works when I punch it into my TI-89, but I can't figure out why...

How about

 

x^(ln y + 1) = exp( (lny + 1)lnx ) = exp (ln x) exp(ln x ln y) = x y^(ln x)

 

Remember that by definition x^alpha is defined as exp (alpha ln x)

 

Mandrake

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