# Solving an equation

1. Aug 29, 2013

### zoxee

how can I solve this using algebraic methods? I know the solution is x = 1 from just looking at it, but not sure how to do it algebraically:

$x + 3^x = 4$

2. Aug 29, 2013

### janhaa

3. Aug 29, 2013

### LeonhardEu

You can set f(x) = x+3^x-4, take x=1 as a solution to f(x) = 0 and look if it is monotonic to show that it has no other solutions. Algebraically is not possible.

4. Aug 29, 2013

### janhaa

a very strange way of writing one:

$$x=\frac{-W(3^4\ln(3))}{\ln(3)}+4=1$$