I feel like such a dope suggesting that the solution could be easily found be inspection.
Actually I was going to suggest the Lambert W-function could be used to get a formal algebraic solution but:
1. I didn't think you had the mathematical background to understand this and didn't want to cause confusion.
2. I didn't want to use an elephant gun to kill a fly.
You will find MHF has many threads showing how the Lambert W-function can be used to solve equations eg.
http://www.mathhelpforum.com/math-he...need-help.html
http://www.mathhelpforum.com/math-he...-equation.html
http://www.mathhelpforum.com/math-he...g-ln-x-kx.html
http://www.mathhelpforum.com/math-he...ed-itself.html
You should have no trouble applying the same idea to your question. You will still get x = 1/3 as the answer but at least you'll be able to justify the solution algebraically.