himpunan penyelesaian pertidaksamaan 2log (x-2)+ 2log (x+5)≤3 adalah.....

Kelas 10 Matematika
Bab Logaritma

^ = pangkat

²log (x - 2) + ²log (x + 5) <= 3
²log ((x - 2) (x + 5)) <= 3
x² + 5x - 2x - 10 <= 2^3
x² + 3x - 10 - 8 <= 0
x² + 3x - 18 <= 0
(x + 6) (x - 3) <= 0
x - 3 <= 0
x <= 3

x + 6 >= 0
x >= -6
-6 <= x

-6 <= x <= 3

syarat
x - 2 > 0
x > 2

x + 5 > 0
x > -5

HP = { x | 2 < x <= 3, x € bilangan real }