Is this solveable? (Natural Log)

[cloudguy]

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?

 

[mmm4444bot]

2*pi*a = e^(-2r) * (2r+1)

Is there a way to solve for 'r' in terms of 'a' here?

Yes, there is. But the explanation goes beyond any algebra class that I ever took.

[attachment=0:1tlw5wxp]LambertW.JPG[/attachment:1tlw5wxp]

 

[cloudguy]

Wow, thanks.

Far beyond algebra indeed. Did you use Mathematica or something to solve that?

 

[mmm4444bot]

Yes. That image is a partial screen shot from software called MapleV Release 5.