³log x +³log (2x-3)<3 Tolong bangett yaa

³log x +³log (2x-3) < 3
³log(x(2x-3)) < ³log27
⇔ x(2x - 3) < 27
⇔ 2x² - 3x - 27 < 0
⇔ (2x - 9)(x + 3) < 0
-3 < x < 9/2

syarat logaritma
x > 0
dan
2x - 3 > 0
2x > 3
x > 3/2

jadi 
HP : {x| 3/2 < x < 9/2}

[tex]^3log x +^3log (2x-3)<3 \\ ^3log x (2x-3)<3 \\ ^3log(2 {x}^{2} - 3x) < ^3log {3}^{3} \\ 2 {x}^{2} - 3x < {3}^{3} \\ 2 {x}^{2} - 3x - 27 < 0 \\ (2 {x} - 9)(x + 3) < 0 \\ \{- 3 < x < \frac{9}{2}\}[/tex]
Ingat syarat logaritma:
[tex]x > 0[/tex]
dan
[tex]2x - 3 > 0 \\ x > \frac{3}{2} [/tex]
jadi himpunan penyelesaian:
[tex]\{ \frac{3}{2} < x < \frac{9}{2} \}[/tex]