SOLUTION: Please help me solve the following equation: 2ln(2x)+ln(3x-2)=ln4x

Question 703581: Please help me solve the following equation:
2ln(2x)+ln(3x-2)=ln4x
Answer by nshah11(47) (Show Source): You can put this solution on YOUR website!
Note that ln(A)+ ln(B) = ln(AB) and Aln(B) = ln(B^A).
2ln(2x) + ln(3x - 2) = ln(4x)
ln(4x^2) + ln(3x - 2) = ln(4x)
4x^2(3x - 2) = 4x
12x^3 - 8x^2 - 4x = 0
4x(3x^2 - 2x - 1) = 0
4x(3x^2 - 3x + x - 1) = 0
4x(3x + 1)(x - 1) = 0
x = 0, -1/3, 1
However only x = 1 will work since the other two values of x lead to a negative argument inside the ln function when plugged back in.
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