nilai x yg memenuhi persamaan [tex] 3^{x+2} + 9^{x+1} [/tex] = 810 adalah

Kelas 10 Matematika
Bab Akar dan Pangkat

^ = pangkat

3^(x + 2) + 9^(x + 1) = 810
3^x . 3² + (3²)^(x + 1) - 810 = 0
9 . 3^x + 3^(2x + 2) - 810 = 0

◎◎ 3^x = p ◎◎

9p + 9p² - 810 = 0
p² + p - 90 = 0
(p + 10) (p - 9) = 0
p + 10 = 0
p = -10
3^x = -10 (tidak memenuhi)

p - 9 = 0
p = 9
3^x = 3²
x = 2