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Math Help - Confirmation of exponential equation answers

  1. #1
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    Confirmation of exponential equation answers

    I did a couple of problems and am just asking if someone could check them for me to see if I got them right.

    Solve for y in terms of t:
    Ln(50-3y)=.5t+ln(5)

    I got : y=(5e^(.5)-50)/-3
    I think I got close but I'm not sure if I have it right

    Ln(10-y)=2t+ln8
    I got : y=-8e^2t +10
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  2. #2
    MHF Contributor Siron's Avatar
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    Re: Confirmation of exponential equation answers

    First one is fine, but try to simplify as much as possible:
    \ln(50-3y)=\frac{1}{2}t+\ln(5)
    \Leftrightarrow e^{\frac{1}{2}+\ln(5)}=50-3y
    \Leftrightarrow y=\frac{50-e^{\frac{1}{2}+\ln(5)}}{3}
    \Leftrightarrow y=\frac{50}{3}-\frac{\sqrt{e}\cdot 5}{3}
    \Leftrightarrow y=\frac{5}{3}\left(10-\sqrt{e}\right)

    Second one is fine!

    \ln(10-y)=2t+\ln(8)
    \Leftrightarrow \ln(10-y)=\ln(e^{2t})+\ln(8)
    \Leftrightarrow \ln(10-y)=\ln(e^{2t}\cdot 8)
    \Leftrightarrow 10-y=e^{2t}\cdot 8
    \Leftrightarrow y=10-e^{2t}\cdot 8
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  3. #3
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    Re: Confirmation of exponential equation answers

    Thanks once again.
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  4. #4
    MHF Contributor Siron's Avatar
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    Re: Confirmation of exponential equation answers

    You're welcome, again!
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