Shouldn't these 2 equations be equal?

[tamtam402]

Homework Statement

I was doing a math problem, where I forgot to simplify e^3ln2.

Homework Equations

The Attempt at a Solution

Instead of doing e^3ln2 = e^{ln(2^3)} = e^ln(8) = 8, I did the following:


e^3ln2 = e³*e^ln2 = 2e³

However, 2e³ ≠ 8.

What happened?
Mod edit: The OP figured it out.

 

[tamtam402]

Just in case someone stumbles here with the same problem, my mistake was to assume e^3ln2 = e³*e^ln2.

That statement is false since e³*e^ln2 = e^3+ln2 ≠ e^3ln2.

 

[HallsofIvy]

Well, let's hope that people who are attempting to solve problems like this will know that $e^{x+ y}= e^xe^y\ne e^{xy}$.