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Math Help - can't solve exponential

  1. #1
    Member i_zz_y_ill's Avatar
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    can't solve exponential

    I am trying to draw x=3e^4t+12e^-t where t is x axis and x is y axis

    I don't understand how from visualising this i can tell it is a growing function and doesntcross the t axis. I drew for instance y = -2e^4t +12e^-t since I knew it would cross the t axis as I could put y=0 and solve it.

    Putting x=o however apparantly cannot be solved. Where am I going wrong,

    0 = 3e^4t + 12e^-t
    -e^4t = 4e^-t
    e^4t = -4e^-t
    lne^4t = -ln4 + lne^-t
    4t = -ln4 -t
    t = -(ln4)/5
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  2. #2
    Lord of certain Rings
    Isomorphism's Avatar
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    Quote Originally Posted by i_zz_y_ill View Post
    e^4t = -4e^-t
    lne^4t = -ln4 + lne^-t
    Wrong!

      e^{4t} = -4e^{-t} \Rightarrow \ln   e^{4t} = \ln(-4) + \ln{e^{-t}} \Rightarrow 4t = \ln(-4) - t \Rightarrow t = \frac{\ln(-4)}{5}

    But actually there is no real number called \frac{\ln(-4)}{5}

    What really should have been done was since e^x > 0, \forall x \in \mathbb{R}

    3e^{4t} > 0 , 12e^{-t} > 0 \Rightarrow x = 3e^{4t}+ 12e^{-t} > 0

    Thus x \neq 0
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