Math Proof: Natural Log (X ^ Y)
Have you ever wondered why the natural log of X to power of Y equals to Y times the natural log of X? In other words, have you ever wondered why this is true?
Wonder no more, because here is the proof.
First, we start off with this equation:
Since X^Y equals to X1 * X2 * .. * XY, then we can re-write the starting equation as:
We know that this statement is true:
Therefore, our equation can be written as:
In other words, this is equal to ln (X) exactly Y times or:
Thatís it! There is your proof for natural log of X to the power of Y is equal to Y times the natural log of X.
by Phil for Humanity