log (2x-1) + log (x+3) = 1 + log 3

Bab Logaritma
Matematika SMA Kelas X

log (2x - 1) + log (x + 3) = 1 + log 3
log ((2x - 1) (x + 3)) = log 10 + log 3
log (2x² + 6x - x - 3) = log (10 . 3)
2x² + 5x - 3 - 30 = 0
2x² + 5x - 33 = 0
(2x + 11) (x - 3) = 0
2x + 11 = 0
2x = -11
x = -11/2

x - 3 = 0
x = 3

syarat
2x - 1 > 0
2x > 1
x > 1/2

Maka, x = 3

log(2x - 1) + log(x + 3) = 1 + log 3
log((2x-1)(x+3)) = log 10 + log 3
log (2x² + 5x - 3) = log 30
⇔ 2x² + 5x - 3 = 30
⇔ 2x² + 5x - 33 = 0
⇔ (2x + 11)(x - 3) = 0
⇔ x = -11/2   atau x = 3

karena x = -11/2 tidak memenuhi jadi, nilai x yang memenuhi adalah
x = 3