# Homework Help: Presumably simple logarithm equationt

1. Feb 6, 2013

### Chase.

1. The problem statement, all variables and given/known data

What value of x satisfies the equation:

6 $\cdot$ e2x = 4x

3. The attempt at a solution

If I'm not mistaken, I can move the 6 to the superscripted part of e, resulting in:

e12x = 4x

And then I can take the natural log of both sides, resulting in:

12x = ln(4x)

Assuming I haven't made any mistakes, this is what I have so far and I'm stuck. This is for a practice test and I have the answer listed as:

ln6 / (ln4 - 2)

I'm just not sure how to get there.

2. Feb 6, 2013

### cepheid

Staff Emeritus
You are mistaken. You can't do that. E.g. 2*32 = 18 ≠ 34 = 81.

Just start with taking the ln of both sides right from the beginning:

ln(6*e2x) = ln(4x)

The log of a product is the sum of the logs:

ln6 + 2x = xln4

Can you take it from here?