# Thread: Need help with Logarithm Problem

1. ## Need help with Logarithm Problem

Here is the problem:

e^4x+3=11

I have pages of work and have looked through my books for clues, but I think I may be thinking about this one wrong. Can anyone help? Thanks.

2. ## Re: Need help with Logarithm Problem

Originally Posted by captaininsano
Here is the problem:

2e^(3x)+5=10

I have pages of work and have looked through my books for clues, but I think I may be thinking about this one wrong. <--- it would be much easier for us to help you if we have some information about your thinking!
Can anyone help? Thanks.
$2e^{3x} + 5=10$

$2e^{3x} =5$

$e^{3x} =2.5$

$3x=\ln(2.5)$

Solve for x.

3. ## Re: Need help with Logarithm Problem

1. Subtract 5 from both side. 2e^(3x)=5
2. Divide both sides by 2. e^(3x)=5/2
3. Take the natural logarithm from both side. 3x=ln(5/2)
4. Divide both sides by 3. x=1/3*ln(5/2)
5. Check the solution.

4. ## Re: Need help with Logarithm Problem

Originally Posted by captaininsano
Here is the problem:

e^4x+3=11
$e^{4x} + 3 = 11$

or

$e^{4x+3} = 11$

?

5. ## Re: Need help with Logarithm Problem

The first one, should have put 4x in parentheses. Sorry.

6. ## Re: Need help with Logarithm Problem

1. Subtract the 3 from both sides. e^(4x)=8
2. Taking the Natural Logarithm both sides and Simplify. 4x=ln(8), 4x=3ln(2)
3. Divide by 4. x=3/4*ln(2).
4. Check the solution.