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Math Help - Problem in my Calc. homework

  1. #1
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    Problem in my Calc. homework

    Solve for t using natural logarithms

    5e^5t=7e^4t

    I tried doing it 3 or 4 times, but I don't seem to be making much progress. The answer is rounded to 3 places.
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  2. #2
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by redsoxfan0825 View Post
    Solve for t using natural logarithms

    5e^5t=7e^4t

    I tried doing it 3 or 4 times, but I don't seem to be making much progress. The answer is rounded to 3 places.
    Take logs of both sides:

    \ln{5e^{5t}}=\ln{7e^{4t}}

    Now use the properties of logs to finish up.
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  3. #3
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    Properties of logarithms, refresh me on those? The highest math I took in HS was trig and I don't think there's anything like this problem in my notes. If you don't have the time, no big deal I'm sure I'll figure it out. Thanks for the help.
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  4. #4
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    5e^{5t} = 7e^{4t}

    5e^{5t} - 7e^{4t} = 0

    e^{4t}(5e^t - 7) = 0

    since e^{4t} > 0 for all t ...

    5e^t = 7

    e^t = \frac{7}{5}

    t = \ln\left(\frac{7}{5}\right)

    you still need to learn the properties of logs ... you'll need them.
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