Presumably simple logarithm equationt

[Chase.]

Homework Statement

What value of x satisfies the equation:

6 \cdot e^2x = 4^x

The Attempt at a Solution

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

e^12x = 4^x

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

12x = ln(4^x)

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.

 

[cepheid]

Homework Statement

What value of x satisfies the equation:

6 \cdot e^2x = 4^x

The Attempt at a Solution

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

e^12x = 4^x

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

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

12x = ln(4^x)

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

ln(6*e^2x) = ln(4^x)

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

ln6 + 2x = xln4

Can you take it from here?