Nilai X yang memenuhi persamaan 2'log(x - 2) = 4'log(x + 28)

Kelas 10 Matematika
Bab Logaritma

^ = pangkat

²log (x - 2) = ^4log (x + 28)
²log (x - 2) = ^(2²)log (x + 28)
²log (x - 2) = (1/2) . ²log (x + 28)
²log (x - 2) = ²log (x + 28)^(1/2)
x - 2 = (x + 28)^(1/2)
(x - 2)² = √(x + 28)²
x² - 4x + 4 = x + 28
x² - 4x - x + 4 - 28 = 0
x² - 5x - 24 = 0
(x - 8) (x + 3) = 0
x + 3 = 0
x = -3

x - 8 = 0
x = 8

Syarat
x - 2 > 0
x > 2

x + 28 > 0
x > -28

Nilai x yang memenuhi = { 8 }