log (2x-4)²- log (x-1) < log (x+4) tolong bantu buatin syarat numerusnya juga, Terima kasih banyak

Simak ya...

log (2x - 4)² - log (x - 1) < log (x + 4)
log (2x - 4)²/(x - 1) < log (x + 4)
(2x - 4)²/(x - 1)] - (x + 4) < 0
samakan penyebutnya
[(2x - 4)² - (x + 4)(x - 1)] / (x - 1) < 0
[4x² - 16x + 16 - x² - 3x + 4] / (x - 1) < 0
[3x² - 19x + 20] / (x - 1) < 0
(3x - 4)(x - 5) / (x - 1) < 0

Pembuat nol
3x - 4 = 0 ---> x = 4/3
x - 5 = 0 ---> x = 5
x - 1 = 0 ---> x = 1

Uji titik
- - .... (1)...+++...(4/3)....- - ...(5)... ++
x < 1 atau 4/3 < x < 5 ........,. (i)

Syarat numerus
(2x - 4)² > 0
2x - 4 > 0
x smua bilangan real , x ≠ 2
.. (ii)

x - 1 > 0
x > 1 ..... (iii)

x + 4 > 0
x > -4 .... (iv)

Nilai x yg memenuhi :
Irisan (i)(ii)(iii)(iv)
4/3 < x < 5