Log(2x2 – 11x + 19) = 1

[tex] log(2x^2-11x+19) = log10 \\ 2x^2 - 11x + 19 = 10 \\ 2x^2 - 11x + 9 = 0 \\ (2x - 9)(x - 1) = 0 \\ x = \frac{9}{2} \\ {atau} \\ x = 1 [/tex]

Bab Logaritma
Matematika SMA Kelas X

log (2x² - 11x + 19) = 1
2x² - 11x + 19 = 10¹
2x² - 11x + 19 - 10 = 0
2x² - 11x + 9 = 0
(2x - 9) (x - 1) = 0
2x - 9 = 0
2x = 9
x = 9/2

x - 1 = 0
x = 1

masukkan nilai x
2x² - 11x + 19 > 0
2 . 1 - 11 . 1 + 19 > 0
2 - 11 + 19 > 0
10 > 0 (memenuhi)

2x² - 11x + 19 > 0
2 . (9/2)² - 11 . (9/2) + 19 > 0
2 . 81/4 - 99/2 + 19 > 0
81/2 - 99/2 + 38/2 > 0
20/2 > 0
10 > 0

maka, x = 1 atau x = 9/2