TITLE: Solve $4 \times2^x+3^x=5^x$ without any sort of calculator
QUESTION [6 upvotes]: Is there a way i can solve the following equation only by using high school mathematics?
$$4 \times2^x+3^x=5^x$$
I tried writing $5$ as $2+3$ but didn't get any result.
After that i tried to divide by $5^x$ and see how the function goes, but, unfortunately didn't got me somewhere either.

REPLY [2 votes]: You tried to use $2+3=5$ to no avail. A slightly different "flash of insight" approach would be to invoke Pythagoras: $3^2+4^2=5^2$.