# Find x

1. Jun 12, 2010

### whysoserious

1. The problem statement, all variables and given/known data
4^x = x^4. My instructor wants me to find the answer that is -0.77, not 2 or 4. And showing work as well.

2. Relevant equations

3. The attempt at a solution

2. Jun 13, 2010

### Immutef

Did you try graphing the equations and finding where they intercept?

Last edited: Jun 13, 2010
3. Jun 13, 2010

### HallsofIvy

There is no "formula" or elementary function that will solve that. I would try to get it into a form in which I could use Lambert's W function- it is defined as the inverse of $xe^x$.

4. Jun 13, 2010

### Axiom17

If you detail you calculations so far perhaps then can advice with this

5. Jun 13, 2010

### whysoserious

I tried using log but I keep getting stuck at xlog2=2logx

6. Jun 13, 2010

### Axiom17

Make a quick sketch of the two functions. Just use the range $-2 \leq x \leq 2$ and plot the two lines together. From the graph you should be able to see the intersect and hence the answer you require.

7. Jun 13, 2010

### HallsofIvy

Why are you ignoring my post? That equation cannot be solved using elementary functions. Do a numerical solution, or graph as Axiom17 and Immutef have suggested, or use Lambert's W function.