Question

Oi pessoas lindas
2 elevado a x +3 = ( 2 elevado a x +2) elevado a 2
Essa equação e de exponenciação me ajudem por favor

Answer 1

Olá Loh345,

use as propriedades da exponenciação:

$a^{m+n}~\to~a^m\cdot a^n\\\\ (a^m})^n~\to~a^{mn}\\\\ \dfrac{1}{a^m}~\to~a^{-m}$

__________________

$2^{x+3}=(2^{x+2})^2\\ 2^x\cdot 2^3=2^{2x+4}\\ 2^x\cdot 8=2^{2x}\cdot 2^4\\ 8\cdot2^x=16\cdot(2^x)^2\\\\ 2^x=k\\\\ 8k=16k^2\\ 16k^2-8k=0~~~~\div~~~~8\\ 2k^2-k=0\\ k(2k-1)=0\\\\ \begin{cases}k'=0~~e~~2k-1=0\\ ~~~~~~~~~~~~~~2k=1\\ ~~~~~~~~~~~~~~k= \dfrac{1}{2} \end{cases}$

$2^x=k\\\\ 2^x=0~~\notin~~\mathbb{R}~~~~~~~~~~~~~~2^x= \dfrac{1}{2}\\\\ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\not2^x=\not2^{-1}\\\\ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~x=-1\\\\ \boxed{S=\{-1\}}$

Tenha ótimos estudos =))