Question

Решите уравнение:
$log_{2} ^{2} x + log _{2} frac{2}{x} = 3$

Answer 1

log²2 x +log2 2/x=3
(log2 x)²+log2 2 - log2 x =3
(log2 x)² - log2 x = 3 -1
log2 x = z
z²-z-2=0
(z-2)(z+1)=0
a) z-2=0, z=2, log2 x =2, x=2², x=4
b)z+1=0, z=-1, log2 x = -1, x= 1/2

Answer 2

Огромное спасибо!!! :)