Pre-Calc

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I am stuck solving this problem, any help please..Many thanks

find all numbers x that satisfy the given equation ln(2x)
------- =2
ln(3x)

  • Pre-Calc -

    ln(2x)/ln(3x)=2
    ln(2x)=2ln(3x)
    ln(2x)=ln(9x²)
    raise to power of e
    eln(2x)=eln(9x²)
    2x=9x²
    x(9x-2)=0
    x=0, or x=2/9
    When working with log equations, always check back to see if the solution results in defined values.
    Log(non-positive number) does not exist.

    Check x=0:
    Both log(2x) and log(3x) give undefined values, and
    Lim x->0 log(2x)/log(3x)=1
    and not 2 as required.

    Check x=2/9:
    log(2*x)/log(3*x)
    =log(4/9)/log(6/9)
    =log(4/9)/log(2/3)
    =2log(2/3)/log(2/3)
    =2 checks.

  • Pre-Calc -

    Thank you mathmate

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