Solve ln(3x+8)=ln(2x+2)+ln(x-2) for x

Question

Please help me.

Answer 1

The natural logarithm equation is ln(3x + 8) = ln(2x + 2) + ln(x - 2).

Apply Product property of natural logarithm : ln u + ln v = ln(uv).

ln(3x + 8) = ln[(2x + 2)(x - 2)].

Apply One - to - One property of natural logarithm : If ln x = ln y then x = y.

3x + 8 = (2x + 2)(x - 2)

3x + 8 = (2x + 2)(x - 2)

3x + 8 = 2x² - 4x +2x - 4

3x + 8 = 2x² - 2x - 4

2x² - 2x - 3x - 8 - 4 = 0

2x² - 5x - 12 = 0

The above equation in the form of quadratic equation : ax² - bx - c = 0.

Substitute the values of a = 2, b = - 5 and c = -12 in the quadratice formula : .

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The solutions .