Question

Log4(x+2)-log4(x-2)=2-log4 8 решите

Answer 1

$log_4(x+2)-log_4(x-2)=2-log_48\\OD3:\\ \left \{ {{x+2\ \textgreater \ 0} \atop {x-2\ \textgreater \ 0}} \right.\\ \left \{ {{x\ \textgreater \ -2} \atop {x\ \textgreater \ 2}} \right. =\ \textgreater \ x\in(2;+\infty)\\\\log_4(x+2)-log_4(x-2)=log_416-log_48\\\\log_4 \frac{x+2}{x-2}=log_4 \frac{16}{8}\\\\log_4 \frac{x+2}{x-2}=log_42\\\\ \frac{x+2}{x-2}=2\\\\2(x-2)=x+2\\\\2x-4=x+2\\\\2x-x=2+4\\\\x=6$

6∈(2;+∞)

ответ: 6