Question

Himpunan penyelesaian pertidaksamaan logaritma 3logx+3log(2x-3)<3 adalah

Answer 1

Verified answer

Bab Logaritma
Matematika SMA Kelas X

³log x + ³log (2x - 3) < 3
³log (x (2x - 3)) < 3
2x² - 3x < 3³
2x² - 3x < 27
2x² - 3x - 27 < 0
(2x - 9) (x + 3) < 0
x + 3 > 0
x > -3
-3 < x

2x - 9 < 0
2x < 9
x < 9/2

-3 < x < 9/2

Syarat
x > 0

2x - 3 > 0
2x > 3
x > 3/2
3/2 < x

HP = { x | 3/2 < x < 9/2, x ∈ bilangan real }