You can put this solution on YOUR website! Given ln(3x+7) + lnx = ln6
We know the property ln(a) + ln(b)= ln(ab)
Therefore, applying the same property, we get
ln [(3x + 7) * x] = 6
Remove the "ln" on both sides, we get
(3x + 7) *x = 6
3x^2 + 7x = 6
3x^2 + 7x - 6 = 0
This is a quadratic equation, we shall solve using factorising,
3x^2 + 9x - 2x - 6 = 0
3x*(x + 3)- 2 *(x + 3) = 0
(3x - 2)(3x -2) = 0
(3x -2) ^2 = 0
Squaring on both sides, we get
(3x -2) = 0
3x = 2
Divide by 3 on both sides, we get
x = 2/3
Hence the value of x = 2/3
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