Question

Resolva a equação log2 (x + 2) + log2 (x-2)= 5

Answer 1

log2(x+2)+log2(x-2)=5

log2(x+2)(x-2)=5 ( propiedade de logaritmo)

(x+2)(x-2)=2^5

x^2-4=32
x^2=36 então x=6 ou x=-6

Answer 2

Boa noite!

Solução!

$log_{2}(x+2)+log_{2}(x-2)=5 \\\\\\ (x+2).(x-2)=2^{5} \\\\\\ ( x^{2} -2x+2x-4)=32 \\\\\\ \\\\\ ( x^{2} -4)=32 \\\\\ x^{2} =32+4\\\\\ x^{2} =36\\\\\ x= \sqrt{36}\\\\\ x=\pm6\\\\\\\\\\ \boxed{Resposta:log_{2}(x+2)+log_{2}(x-2)=5~~~~x=\pm6}$

Boa noite!
Bons estudos!