Jumlah semua penyelesaian dari persamaan 9^(8x−9)⋅(3ˣ)²=(1/27^(x−1))²ˣ adalah …

Jumlah semua penyelesaian dari persamaan 9^(8x−9)⋅(3ˣ)²=(1/27^(x−1))²ˣ adalah …
A. -2
B. 2
C. 1
D. -1
E. 0

Jawaban : -2

Penyelesaian:
Konsep :
Ubah jadi 3^m = 3^n
Maka m=n

9^(8x−9)⋅(3ˣ)²=(1/27^(x−1))²ˣ
(3²)^(8x−9)⋅(3²ˣ)=(1²ˣ/(3³)^(x−1)(2x)
3^(2(8x-9)+2x) = 3^ (-3(x-1)(2x))
3^(16x-18+2x) = 3^(-6x²+6x)
Maka
16x-18+2x = -6x²+6x
18x – 18 = -6x²+6x
6x²-6x+18x-18=0
6x²+12x-18 = 0 (bagi dengan 6)
x²+2x-3 = 0
(x+3)(x-1) = 0

• x+3=0
x = -3 ==> x1 = -3

• x-1 = 0
x = 1 ==> x2 = 1

Sehingga
x1+x2 = -3+1
= -2

Kesimpulan, Jumlah semua penyelesaian dari persamaan 9^(8x−9)⋅(3ˣ)²=(1/27^(x−1))²ˣ adalah -2

Semoga membantu ya.

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