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

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To solve the logarithmic problem using the Change of Base Formula, Pete can start by recognizing that x^(log base x of y) simplifies directly to y. This follows from the definition of logarithms, where log_x(y) indicates the exponent to which x must be raised to yield y. By applying the property that x raised to the logarithm base x of y equals y, Pete can confidently conclude that x^(log_x(y)) = y. Understanding this relationship eliminates confusion about the cancel-out rule in logarithmic expressions. Thus, Pete can effectively solve the problem using his knowledge of logarithmic definitions and properties.
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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) =
 
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What is the definition of a logarithm ?
 
log base b of n = x <=> b^x = n
 
Let
\xi = \log_x y
\Leftrightarrow x ^ {\xi} = y, right?
So:
x ^ {\log_x y} = x ^ {\xi} = ?
Can you go from here? :)
 
Thanks! (Previously I knew the cancel-out-rule, but I didn't understand why you can cancel.)
 
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