Question

Tentukan himpunan penyelesaian dari perasamaan logaritma berikut:
log (2x+1)+log (x-3)=log(x2-7)

Answer 1

Log(2x+10)+log(x-3)=Log(2x-7)
Log(2x+10)(x-3)=log(2x-7)
(2x+10)(x-3)=(2x-7)
2x²+4x-30=2x-7
2x²+2x=23
2x(x+1)=23
2x=23 atau x+1=23
x=23/2 atau x=22

Answer 2

Log {(2x+1)(x-3)} = log (x^2-7)
(2x+1)(x-3) = (x^2-7)
2x^2 - 6x + x - 3 = x^2 - 7
2x^2 - x^2 - 5x - 3 + 7 = 0
x^2 - 5x + 4 = 0
(x - 1) (x + 5) = 0