ln(3x-2)+ln(x-4)=ln8

Question

solve ln(3x-2)+ln(x-4)=ln8

Answer 1

ln((3x-2)(x-4))=ln(8)⇒(3x-2)(x-4)=8,

3x²-14x+8=8,

3x²-14x=0,

x(3x-14)=0, eliminate x=0, because we would be attempting to take logs of negative numbers, so 3x-14=0, x=14/3.

If we substitute x=14/3 into the original equation we get:

ln(12)+ln(14/3-4)=ln(8),

ln(12×⅔)=ln(8), so x=14/3 is the only solution.