SOLUTION: ln(x^3)-ln(2-(3/2)x)=ln(2x), solve for x.

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Question 748218: ln(x^3)-ln(2-(3/2)x)=ln(2x), solve for x.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
ln%28x%5E3%29-ln%282-%283%2F2%29x%29=ln%282x%29

ln%28x%5E3%29-ln%28%284-3x%29%2F2%29=ln%282x%29........since ln%28%284-3x%29%2F2%29=ln%284-3x%29-ln%282%29, we will have

ln%28x%5E3%29-%28ln%284-3x%29-ln%282%29%29=ln%282x%29
ln%28x%5E3%29-ln%284-3x%29%2Bln%282%29=ln%282x%29

ln%28x%5E3%29%2Bln%282%29=ln%282x%29%2Bln%284-3x%29

ln%282x%5E3%29=ln%282x%284-3x%29%29
2x%5E3=2x%284-3x%29
cross%282%29x%5Ecross%283%29=cross%282%29cross%28x%29%284-3x%29
x%5E2=4-3x
x%5E2%2B3x-4=0

x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+

x+=+%28-3+%2B-+sqrt%28+3%5E2-4%2A1%2A%28-4%29+%29%29%2F%282%2A1%29+

x+=+%28-3+%2B-+sqrt%28+9%2B16+%29%29%2F2+
x+=+%28-3+%2B-+sqrt%2825+%29%29%2F2+

x+=+%28-3+%2B-+5%29%2F2+
solutions:
x+=+%28-3+%2B+5%29%2F2+
x+=+2%2F2+
x+=1+......real solution

x+=+%28-3+-+5%29%2F2+
x+=+-8%2F2+
x+=-4+.....assuming a complex-valued logarithm