# Solve for x (3^x = x^2)

## Homework Statement

Find all possible values of x:

x2 = 3x

## The Attempt at a Solution

I took the log of both sides.. didn't get anywhere. I'm not sure where to start.

You can't solve this analytically with logarithms. You can either guess the right answer and prove that it works, use the Lambert W function or you can use a numerical method.

okays... thanks a lot!

dextercioby
Homework Helper
Your equation has a solution, because both functions are monotone and increasing.

$$3^{-1}<(-1)^2$$

$$3^0 > 0^2$$

D H
Staff Emeritus
$$x=-\sqrt{3^x}$$