This question already has an answer here:
So lately I came across this seemingly simple problem that I just can't get around. Solve this equation:
$x^2 = 2^x$
I cannot do this algebraically, while I refuse to believe it is impossible to solve this algebraically or at least without a graphic calculator (maybe use Newton's method or series approximations?).
I decided to simplify the problem:
$x = 2^x$
Again, I cannot find an exact way to solve this.