Nilai x yang memenuhi persamaan 1/2 log(x2-3)-1/2logx= -1 adalah?

Kelas 10 Matematika
Bab Logaritma

^ = pangkat

^(1/2)log (x² - 3) - ^(1/2)log x = -1
^(1/2)log ((x² - 3)/x) = -1
(x² - 3)/x = (1/2)⁻¹
x² - 3 = 2x
x² - 2x - 3 = 0
(x - 3) (x + 1) = 0
x - 3 = 0
x = 3

x + 1 = 0
x = -1

Syarat
x² - 3 > 0
(x + √3) (x - √3) > 0
x - √3 > 0
x > √3

x + √3 < 0
x < -√3

x > 0

Maka, nilai x yang memenuhi, x = 3