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Math Help - HELP W/ Natural Log

  1. #1
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    HELP W/ Natural Log

    ln(5x-2) = ln6 - ln(x-3)

    Thanks!
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  2. #2
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    Quote Originally Posted by felixthecat12b View Post
    ln(5x-2) = ln6 - ln(x-3)

    Thanks!
    Rewrite with you log rules to get

    \ln(5x-2)=\ln\left( \frac{6}{x-3}\right)

    Since both sides are the same natural log the arguments must be equal

    5x-2=\frac{6}{x-3} Clearing the fraction we get

    (x-3)(5x-2)=6 \iff 5x^2-17x+6=6 \iff 5x^2-17x=0

    x(5x-17)=0 so we get the two solutions x=0 \\\ x=\frac{17}{5}

    x cannot be zero why? hmmm but the other will work.

    I hope this helps.

    Good luck.
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