Question

Логарифм. Реши уравнениe, используя метод подстановки.(с ОДЗ) пошагово

Answer 1

ОДЗ : x > 0

$1+log_{2}^{2}x=log_{2}(8x)\\\\1+log_{2}^{2}x=log_{2}8+log_{2}x \\\\1+log_{2}^{2}x=log_{2}2^{3} +log_{2}x\\\\1+log_{2}^{2}x=3log_{2}2 +log_{2}x\\\\1+log_{2}^{2}x=3+log_{2}x\\\\log_{2}^{2}x-log_{2}x-2=0\\\\log_{2} x=m\\\\m^{2}-m-2=0\\\\m_{1}=-1\\\\m_{2} =2- \ teorema \ Vieta\\\\1)log_{2}x=-1\\\\x_{1}=0,5\\\\2)log_{2}x=2\\\\x_{2}=4\\\\Otvet:\boxed{0,5 \ ; \ 4}$