How can Pete solve a logarithmic problem using the Change of Base Formula?

[Helicobacter]

Pete has access to a scientific calculator and only knows the Definition of a Logarithm and the Change of Base Formula. How is Pete able to solve the following problem?:

x^(log base x of y) =

 

[Curious3141]

What is the definition of a logarithm ?

 

[Helicobacter]

log base b of n = x <=> b^x = n

 

[VietDao29]

Let
$$\xi = \log_x y$$
$$\Leftrightarrow x ^ {\xi} = y$$, right?
So:
$$x ^ {\log_x y} = x ^ {\xi} = ?$$
Can you go from here? :)

 

[Helicobacter]

Thanks! (Previously I knew the cancel-out-rule, but I didn't understand why you can cancel.)