Nilai x yang memenuhi persamaan 1/2log(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 + 2) = 0
x - 3 = 0
x = 3

x + 2 = 0
x = -2

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

x - √3 > 0
x > √3

x > 0

Nilai x yang memenuhi, x = 3