# How do you solve this problem involving e?

• Aug 29th 2008, 08:06 PM
MegaVortex7
How do you solve this problem involving e?
The problem is:
4e^(2x)=5

Solve for e. I did this using logs, and I got a decimal approximation, but my teacher said that the answer was (ln(5/4))/2. Can anyone help me? I don't really know how to use natural logs- do they have different rules than regular logs?
• Aug 29th 2008, 08:17 PM
mr fantastic
Quote:

Originally Posted by MegaVortex7
The problem is:
4e^(2x)=5

Solve for e. I did this using logs, and I got a decimal approximation, but my teacher said that the answer was (ln(5/4))/2. Can anyone help me? I don't really know how to use natural logs- do they have different rules than regular logs?

1. You're solving for x, not e.
2. You ought to know that all logs use the same rule. What logs do you know how to use?
3. What you're really saying is that you used a calculator to get a decimal approximation to the exact answer when you were meant to use algebra to get an exact answer.

$\displaystyle 4 e^{2x} = 5 \Rightarrow e^{2x} = \frac{5}{4}$.

Now apply the definition $\displaystyle A^B = C \equiv \log_A C = B$ (for all values of A > 0 except A = 1). In your case A = e.
• Aug 30th 2008, 06:44 AM
MegaVortex7
Right right, I meant x. Sorry. And thank you SO much!
• Sep 1st 2008, 08:01 AM
Showcase_22
I did it this way:

http://i116.photobucket.com/albums/o...sproblem11.jpg

I put some of the handy rules on there. Just remember those and you can blitz these questions!(Cool)