In(5x-1)=in(3x+2) extraneous solution

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In(5x-1)=in(3x+2) extraneous solution

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Clara 2 weeks 2021-10-11T18:43:34+00:00 1 Answer 0

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    2021-10-11T18:45:07+00:00

    \ln(5x-1)=\ln(3x+2)

    First note that the left side exists only for 5x-1>0, or x>\dfrac15, and the right side exists only for 3x+2>0, or x>-\dfrac23. Then any solution to this equation is extraneous if we find x\le\dfrac15.

    Write both sides as powers of e to eliminate the logarithms:

    e^{\ln(5x-1)}=e^{\ln(3x+2)}\implies5x-1=3x+2

    Simplify and solve:

    2x=3\implies x=\dfrac32

    No extraneous solutions here because the one found is larger than 1/5.

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