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Thread: Solving Exponential Equations

  1. #1
    Newbie Auger's Avatar
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    Solving Exponential Equations

    Question is in the link. I just can't figure these 2 out.
    Thanks a lot....again!

    http://img9.imageshack.us/img9/7561/60225025.jpg (that exponent on the second equation is a -t)

    Auger
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  2. #2
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    e^(i*pi)'s Avatar
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    Quote Originally Posted by Auger View Post
    Question is in the link. I just can't figure these 2 out.
    Thanks a lot....again!

    http://img9.imageshack.us/img9/7561/60225025.jpg (that exponent on the second equation is a -t)

    Auger
    $\displaystyle (\frac{1}{32})^{4x} = 1024$

    All these numbers are powers of two so it can be expressed as:

    $\displaystyle \frac{1}{2^{20x}} = 2^{-20x} = 2^{10}$

    If the bases are equal then the exponents must be equal: $\displaystyle -20x = 10$. Should be clear that $\displaystyle x = -0.5$

    -------------------

    $\displaystyle \frac{20}{3+4e^{-t}} = 5$

    Take the reciprocal of both sides and then multiply by 20

    $\displaystyle 3+4e^{-t} = 4$

    Take 3 and then divide by 4:

    $\displaystyle e^{-t} = \frac{1}{4}$

    $\displaystyle -t = -ln(4) = -2ln(2)$

    $\displaystyle t = 2\,ln2$
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  3. #3
    Newbie Auger's Avatar
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    sorry i don't understand how you got to the second step. I have not learnt this. Could you explain?

    thanks
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