(4^x)+(5^x)=6^x

[jdouglasusn]

I'm having a ***** of a time with this. I know it will need logarithms.
Thanks in advance. No I'm not a student that need help with homework. I'm at work and we like putting problems on the board. However I like to know how to solve one before I put it up there. I have a feeling this might be complex.

(4^x)+(5^x) = 6^x

Thanks in advance.

[stapel_eliz]

You might want to look up "Fermat's Last Theorem" before investing too much time trying to find a whole-number solution. For non-whole-number solutions, a graph will probably be helpful. An approximation of the solution to this non-algebraic equation will likely be about as good as you can get.