Question

log2(x-5)+log2(x+2)=3

Answer 1

ОДЗ
$left { {{x-5 textgreater 0} atop {x+2 textgreater 0}} right. \ \ left { {{x textgreater 5} atop {x textgreater -2}} right. \ \ x textgreater 5$

$log_2(x-5)+log_2(x+2)=3 \ \ log_2(x-5)(x+2)=3 \ \ (x+2)(x-5)=2^3 \ \ x^{2} -5x+2x-10=8 \ \ x^{2} -3x-18=0 \ \ D=3^2+4*18= 81 \ \ x_1= frac{3+9}{2}=6 \ \ x_2=frac{3-9}{2}=-3$

х₂=-3 не удовлетворяет ОДЗ

Ответ х=6