Question

Estou tendo problemas com este cálculo, devido ao mmc de 52.
Obs: Função exponencial.

Answer 1

$2^{x-3}+2^{x-1}+2^x~=~52\\\\\\2^x.2^{-3}+2^x.2^{-1}+2^x.1~=~2~.~2~.~13\\\\\\2^x.(2^{-3}+2^{-1}+1)~=~2^2~.~13\\\\\\\frac{2^x(\frac{1}{8}+\frac{1}{2}+1)}{2^2}~=~13\\\\\\2^x.(\frac{13}{8})~.~2^{-2}~=~13\\\\\\2^x.(\frac{13}{2^3})~.~2^{-2}~=~13\\\\\\13~.~2^x.\frac{1}{2^3}.2^{-2}~=~13\\\\\\2^{\,x-3+(-2)}~=~\frac{13}{13}\\\\\\2^{x-5}~=~1\\\\\\2^{x-5}~=~2^0\\\\\\x-5~=~0\\\\\\\boxed{x~=~5}$