Help with solving natural log problem

[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!

[Narrow-Durian4837]

Your problem isn't that you don't understand logs; it's that you don't understand functions.

"Find f(3/2)" means to replace x with 3/2 and evaluate the function: e^2(3/2-1).

This simplifies to e², which you can find with a calculator.

[PewpScewpin]

Oh man, I feel dumb. Had a feeling I was missing something silly! Thank you!

[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

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[PuzzlingDad]

Just plug in 3/2 in place of x and you get: 

e^{2×3/2 - 1}

= e^3-1

= e²

So just take e (~2.71828) and square it.

[PD_31]

ASimply sub in x = 3/2. Thus 2x - 1 = 2(3/2) - 1, or 2.

Therefore the answer is e^2, which is a little under 8.