Question

4 elevado a x+1 x 8 elevado a 2x -3 =(2 elevado a 1 + x) / 16

Answer 1

Use as propriedades da exponenciação,

$a^{m+n}\Rightarrow a^m\cdot a^n\\\\ \dfrac{a^m}{a^n}\Rightarrow a^m\cdot a^{-n}\\\\ (a^m)^n\Rightarrow (a^{m\cdot n})$

$4^{x+1}\cdot8^{2x-3}= \dfrac{2^{1+x}}{16}\\ (2^2)^{x+1}\cdot(2^3)^{2x-3}= \dfrac{2^{1+x}}{2^4}\\\\ 2^{2x+2}\cdot2^{6x-9}= 2^{1+x}\cdot2^{-4}\\ 2^{2x+2+6x-9}=2^{1+x-4}\\ \not2^{8x-7}=\not2^{x-3}\\\\ 8x-7=x-3\\ 8x-x=-3+7\\ 7x=4\\\\ x= \dfrac{4}{7}\\\\\\ \Large\boxed{S=\left\{ \dfrac{4}{7}\right\}}$

Espero ter ajudado e tenha ótimos estudos. Qualquer dúvida me chame ^^