I need help finding the correct answer. I got it wrong on my homework and am studying for my test and need to know how to do it.

Question

ln e^lnx-ln(x-3)=ln 8
my wrong answer - no solution
correct answer - (24/7)

Answer 1

ln e^lnx-ln(x-3)=ln8

First of all the "ln of e" cancels out, so it is just:

ln(x)-ln(x-3)=ln(8)

which is the same as:

ln(x/(x-3))=ln(8)

e^ both sides...

x/(x-3)=8
x=8x-24
7x=24
x=24/7