Question

1 ) 5log (x²- 4) < 1

2) ½log (x - 0) < ½log (3x - 2)

3) 5log (2x²+5x-3) > 5log (x²+2x-3)

4) 3log 3x = 3log (x+2)

Answer 1

Verified answer

LogAritMa

1][
5'log (x² - 4) < 1
5'log (x² - 4) < 5'log 5
x² - 4 < 5
x² < 4 + 5
-3 < x < 3 ... (1)

x² - 4 > 0
x² > 4
x < -2 atau x > 2 ... (2)

Nilai x yg memenuhi :
Irisan (1) dan (2)
-3 < x < -2 atau 2 < x < 3

2]
½'log (x - 0) < ½'log (3x - 2)
x > 3x - 2
x - 3x > -2
-2x > -2
x < 1 ... (1)

x > 0 ... (2)

3x - 2 > 0
x > 2/3 ... (3)

Nilai x yg memenuhi :
Irisan (1) (2) dan (3)
2/3 < x < 1

3][
5'log (2x² + 5x - 3) > 5'log (x²+ 2x - 3)
2x² + 5x - 3 > x² + 2x - 3
x² + 3x > 0
x(x + 3) > 0
x < -3 atau x > 0 ... (1)

2x² + 5x - 3 > 0
(2x - 1)(x + 3) > 0
x < -3 atau x > 1/2 ... (2)

x² + 2x - 3 > 0
(x + 3)(x - 1) > 0
x < -3 atau x > 1 ... (3)

Nilai x yg memenuhi :
Irisan (1) (2) dan (3)
x < -3 atau x > 1

4][
3'log 3x = 3'log (x + 2)
3x = x + 2
2x = 2
x = 1