Let $f(x)=2^x+5^x-7^x$. The problem is to study the monotonicity intervals of $f(x)$.
My first attempt to tackle the above, is to study the sign of the derivative of $f(x)$
$f^\prime (x)=ln(2)\cdot 2^x+ln(5)\cdot5^x-ln(7)\cdot7^x$
However I can see no obvious way of proceeding. Any ideas would be appreciated