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Math Help - Help me tO solve this algebra..please

  1. #1
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    Help me tO solve this algebra..please

    Solve 3 In 2x =3 + In 27
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  2. #2
    MHF Contributor MarkFL's Avatar
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    Re: Help me tO solve this algebra..please

    I am assuming you mean \ln and not \text{In}. We are given:

    3\ln(2x)=3+\ln(27)

    I would rewrite this as:

    3\ln(2x)=3+\ln(3^3)

    so that we may use the property \log_a(b^c)=c\cdot\log_a(b) to then rewrite the equation as:

    3\ln(2x)=3+3\ln(3)

    Next, divide through by 3:

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

    Next, use the fact that \ln(e)=1 to write:

    \ln(2x)=\ln(e)+\ln(3)

    To finish now, on the right use the property \log_a(b)+\log_a(c)=\log_a(bc), then equate the resulting arguments, then solve for x.
    Thanks from sharmala
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  3. #3
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    Re: Help me tO solve this algebra..please

    another method
    3ln(2x) =3 +ln(27)
    ln (2x/3)^3 =3
    e^3 =(2x/3)^3
    e = 2x/3
    e = 2.303
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