Solve equations like $3^x+4^x=7^x$ How can I solve something like this?
$$3^x+4^x=7^x$$
I know that $x=1$, but I don't know how to find it. Thank you!

By putting  the given equation in the form:
$$ {\left( \dfrac {3}{3+4} \right )  } ^x  +  {\left( \dfrac {4}{3+4} \right )  } ^x =1 $$ 
we find it is satisfied by $x=1$. The monotonic nature of exp function gives no other real roots.
