# Can this problem be solved? (Natural Log)

• Sep 1st 2010, 03:26 PM
cloudguy
Can this problem be solved? (Natural Log)
I have this equation that needs to be solved for 'r'
2*pi*a = e^(-2r) * (2r+1)
The variable a is a constant but I need to solve for r in terms of a. I was going to take the natural log of both sides to eliminate the exponential, but that will end up putting the other r inside of a natural log function.
Is there a way to solve for 'r' in terms of 'a' here?
• Sep 1st 2010, 03:37 PM
pickslides

$\displaystyle2\pi a = e^{(-2r) (2r+1)}$

or is it

$\displaystyle2\pi a = e^{-2r }(2r+1)$
• Sep 1st 2010, 03:50 PM
cloudguy
The second one, sorry.
• Sep 1st 2010, 03:53 PM
pickslides
I don't see a way.
• Sep 1st 2010, 03:55 PM
cloudguy
Thanks. I didnt either.
• Sep 1st 2010, 04:33 PM
Ackbeet
There are two special solutions, plus the product logarithm function solution. See here.