Solve 4^x = x^4: -0.77 Answer w/Work

[whysoserious]

Homework Statement

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.

Homework Equations

The Attempt at a Solution

 

[Immutef]

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

 

[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.

 

[Axiom17]

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

 

[whysoserious]

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

 

[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.

 

[HallsofIvy]

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

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.