²log(x+1) + ²log(x-2)=3

Persamaan Logaritma

²log (x + 1) + ²log (x - 2) = 3
²log ( (x + 1)(x - 2) ) = 3
(x + 1)(x - 2) = 2³
x² - x - 2 = 8
x² - x - 10 = 0

D = (-1)² - 4 . 1 . -10
D = 1 + 40
D = 41

x = ( -(-1) ± √41) /2
x = (1 + √41) /2
x = (1 - √41)/2

Telaah bagian bil.yang dilogaritmakan

syarat : jika ^a log b = c
b > 0

Telaah :

x + 1 > 0
x > -1

x - 2 > 0
x > 2

Irisan ny x > 2

yg memenuhi :

x = [tex] \dfrac{1 + \sqrt{41}}{2} [/tex]