Question

log (x^2 +4x-5) по основанию 1/2 = -3

Answer 1

ОДЗ:
$x^2+4x-5 textgreater 0 \ (x-1)(x+5) textgreater 0$
x∈(-∞;-5)∪(1;+∞)

$log_ frac{1}{2} (x^2+4x-5)=-3 \ x^2+4x-5=( frac{1}{2})^-^3 \ x^2+4x-5=8 \ x^2+4x-13=0 \ D=16+52=68=2 sqrt{17} \ \ x_1= frac{-4-2 sqrt{17} }{2}=-2- sqrt{17} \ \ x_2= frac{-4+2 sqrt{17} }{2}=-2+ sqrt{17}$