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Math Help - Problem with solving equation

  1. #1
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    Problem with solving equation

    Having trouble with a section in my summer assaignment, and my teacher doesnt respond to his e-mails... If someone could help with these few questions, it would help a lot. Thanks.

    Solve for y in terms of t:

    -2e^(-y/3)=t+4

    -t/4)-ln3=ln(20-y)

    I know for the 2nd question you need to combine to take the anti-log(I beleive), but I just dont know where. And I have no idea where to start on the first problem.
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  2. #2
    MHF Contributor Siron's Avatar
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    Re: Problem with solving equation

    For the first one, take the \ln of both sides so you get:
    \ln\left(2e^{-\frac{-y}{3}}\right)=\ln(t+4)
    Now use the fact \log(a^b)=b\cdot \log(a)
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  3. #3
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    Re: Problem with solving equation

    You put a negative symbol before the (y/3). Could you tell me where you got that from?
    Did you get it from the -2e from the begining and moved it to the exponent when you multiplied by the ln?

    Also that would make -y/3 = (ln2e) X ((ln t+4))? e would have to be raised by somethig though, so I know that isnt right... but I'm hoping its something along those lines.
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  4. #4
    MHF Contributor Siron's Avatar
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    Re: Problem with solving equation

    Sorry, I didn't see that. That's indeed a mistake. Indeed you get:
    \ln(2)-\frac{y}{3}=\ln(t+4) \Leftrightarrow -\frac{y}{3}=\ln(t+4)-\ln(2) \Leftrightarrow -\frac{y}{3}=\ln\left(\frac{t+4}{2}\right) \Leftrightarrow y=-3\ln\left(\frac{t+4}{2}\right)

    For the second one I would use the definition:
    \log_a(x)=y \Leftrightarrow a^y=x
    So in this case:
    \frac{t}{4}-\ln(3)=\ln(20-y) \Leftrightarrow e^{\frac{t}{4}-\ln(3)}=20-y \Leftrightarrow ...
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  5. #5
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    Re: Problem with solving equation

    Ahh, that makes sense. Thank you so much.
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  6. #6
    MHF Contributor Siron's Avatar
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    Re: Problem with solving equation

    You're welcome!
    Notice you can simplify the second one:
    \frac{t}{4}-\ln(3)=\ln(20-y)
    \Leftrightarrow e^{\frac{t}{4}-\ln(3)}=20-y
    \Leftrightarrow y=20-e^{\frac{t}{4}-\ln(3}}
    \Leftrightarrow y=20-\frac{e^{\frac{t}{4}}}{e^{\ln(3)}}
    \Leftrightarrow y=20-\frac{e^{\frac{t}{4}}}{3}
    \Leftrightarrow y=20-\frac{\sqrt[4]{t}}{3}
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  7. #7
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    Re: Problem with solving equation

    That helps a lot! Thank you once again!
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