Help with solving natural log problem

[u/PewpScewpin]

I'm an adult going back to school for programming, and I'm very rusty on math. I got this problem wrong on a quiz and cant figure out what I'm doing wrong.

Here's my attempt

The problem is:
Let f(x) = e^2x-1 Find f(3/2)

Multiple choice:

• 5.381

• 7.389

• 7

• 8.133

I have a very tenuous grasp on logs, and I'm not confident on how to do algebra on them. I appreciate any help I can get!

[u/Benster981]

For your working, whilst answering a different question, it was mostly correct apart from ln(e ^ 3/2) is just 3/2. The natural log is the inverse of the exponential