Question

Resolva a equação exponencial: 8ˣ/2ˣ⁺2=256

Answer 1

Lembrando das seguintes propriedades

$\large\fbox{ (a^m)^n=a^{m\cdot n} }\\\\\large\fbox{ \dfrac{a^m}{a^n}=a^{m-n}~~~~(a\neq 0~~e~~m \geq n) }\\\\\large\fbox{ a^b=a^c\Longleftrightarrow b=c~~~~(0\ \textless \ a \neq 1) }$

O que temos é 

$\dfrac{8^x}{2^{x+2}}=256~\Leftrightarrow~\dfrac{(2^3)^x}{2^{x+2}}=2^8~\Leftrightarrow~\dfrac{2^{3x}}{2^{x+2}}=2^8~\Leftrightarrow~2^{(3x-x)-2}=2^8\\\\\\2^{2x-2}=2^8~\Longleftrightarrow~2x-2=8~\Leftrightarrow~2x=10~\Leftrightarrow~x=\dfrac{10}{2}\\\\\\\fbox{ x=5 }$