# Homework Help: Solving equation with power of x in it

1. Jan 5, 2012

### Froskoy

1. The problem statement, all variables and given/known data
$$x^2+1=2^x$$

2. Relevant equations
N/A

3. The attempt at a solution
$$x^2 + 1 = 2^x$$
$$\log_2(x^2+1) = log_22^x$$
$$log_2(x^2+1)=x$$

With very many thanks,

Froskoy.

2. Jan 5, 2012

### micromass

This equation cannot be solved analytically. There is no technique to find the correct answer. Either you

1) Guess a solution and prove that it is the correct one.
2) Use the Lambert W function to find an expression for the solution.
3) Find a solution numerically.

(1) will work here. But it remains to prove here that the guessed solutions are the only solutions.

3. Jan 5, 2012

### ehild

Plotting both sides would help to find all three roots.

ehild

4. Jan 5, 2012