Proofing Logarithms: a^(log(b))=b^(log(a))

[eric123]

Does anyone know how to proof the following:

a^(log(b))=b^(log(a))

for a,b>0

 

[Mark44]

Let x = a^{log b} and y = b^{log a}

Using the rules of logarithms, show that log x = log y, hence that a^{log b} = b^{log a}

 

[eric123]

thanks