Question

Himpunan penyelesaian persamaan dari log²(x+2) + log(x+2)²= log 0,1 adalah...

Answer 1

Verified answer

log²(x+2) + log(x+2)² = log 0,1
= log²(x+2) + 2 log(x+2) = log 10⁻¹
= log²(x+2) + 2 log(x+2) = -1 . log10
= log²(x+2) + 2 log(x+2) = -1
misalkan
y = log(x + 2)
maka bentuk pers menjadi
y² + 2y + 1 = 0
(y + 1)² = 0
y = -1

y = -1
log(x + 2) = -1
log(x + 2) = log(1/10)
x + 2 = 1/10
x = 1/10 - 20/10
x = -19/10