I am doing some math repetition and am a bit stuck on this exercise:
Solve the equation: $1+2^x+4^x+8^x+16^x+32^x=3(1+2^x+4^x)$.
Now, this is a geometric sum on both the $LHS$ and $RHS$, which I guess is something that I should use to solve the equation...
Another way is to simply start to eliminate terms:
$$1+2^x+4^x+8^x+16^x+32^x=3+3 \times 2^x+3\times4^x$$
$$-2 -2\times 2^x -2\times4^x+8^x+16^x+32^x = 0$$
$$8^x+16^x+32^x = 2 +2\times 2^x +2\times4^x$$
$$8^x+16^x+32^x = 2(1 + 2^x + 4^x)$$
But I am stuck here...