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Math Help - Logarithm help

  1. #1
    Newbie Twilight's Avatar
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    Logarithm help

    I understand the basics, but I can't figure this one out. Any help would be appreciated.

    Give the exact answer ( in terms of natural logarithms). Then use a calculator to find an approximat answer.

    7.8e^(x/3)ln5 = 14


    Thank you for your time.
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Twilight View Post
    I understand the basics, but I can't figure this one out. Any help would be appreciated.

    Give the exact answer ( in terms of natural logarithms). Then use a calculator to find an approximat answer.

    7.8e^(x/3)ln5 = 14


    Thank you for your time.
    If you want an exact answer then turn the decimal into a fraction first:
    7.8 = \frac{78}{10} = \frac{39}{5}

    My question, though, is whether the "ln(5)" is part of the exponent, or multiplying the e^(x/3)?

    -Dan
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  3. #3
    Newbie Twilight's Avatar
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    It is part of the exponent. Sorry that was not clear.
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  4. #4
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    Quote Originally Posted by Twilight View Post
    I understand the basics, but I can't figure this one out. Any help would be appreciated.

    Give the exact answer ( in terms of natural logarithms). Then use a calculator to find an approximat answer.

    7.8e^(x/3)ln5 = 14


    Thank you for your time.
    If the equation is 7.8 e^{\frac{x \ln 5}{3}} = 14 then that's one helluva ugly exact answer .......

    Picking up from topsquark:

    e^{\frac{x}{3} \ln 5} = \frac{70}{39}


    \therefore \frac{x}{3} \ln 5 = \ln \frac{70}{39}


    \therefore x \ln 5 = 3 \ln \frac{70}{39}


    \therefore x = \frac{3 \ln \frac{70}{39}}{\ln 5}


    \therefore x = ...... Only kidding!! log/log CANNOT BE SIMPLIFIED - engrave (*ahem* metaphorically speaking) this fact on your skull.
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