Algebra

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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.

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

  • Algebra -

    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

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