# Basic Logarithmic Problem

1. Apr 7, 2006

### 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) =

Last edited: Apr 8, 2006
2. Apr 8, 2006

### Curious3141

What is the definition of a logarithm ?

3. Apr 8, 2006

### Helicobacter

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

4. Apr 8, 2006

### VietDao29

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

5. Apr 8, 2006

### Helicobacter

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