Proving the Inverse Relationship of ln(x) and e^x

[appplejack]

Homework Statement

How do you prove ln(e^x) = x?

Homework Equations

The Attempt at a Solution

I just memorized this but want to know how I can prove this

 

[Dick]

It's the definition of ln(x) that it is the inverse of e^x. If you want another way then ln(e^x)=x*ln(e). What's ln(e)?