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Thread: Exponential Function

  1. #1
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    Exponential Function

    If $\displaystyle 13^{-x}=10$, what does $\displaystyle 13^{2x}$ equal?

    Answer is:
    $\displaystyle 13^{2x}=\frac{1}{100}$

    How do you solve this?

    $\displaystyle
    \frac{log 13}{log x} = 10
    $

    Is that the right start?
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  2. #2
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    Some progress..

    $\displaystyle
    \frac{13}{13x}=10
    $

    $\displaystyle
    13=10(13^x)
    $

    $\displaystyle
    13=130^x
    $

    $\displaystyle
    \frac{13}{130}=x
    $

    $\displaystyle
    \frac{1}{10}=x
    $
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  3. #3
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    Quote Originally Posted by desiderius1 View Post
    If $\displaystyle 13^{-x}=10$, what does $\displaystyle 13^{2x}$ equal?

    Answer is:
    $\displaystyle 13^{2x}=\frac{1}{100}$

    How do you solve this?

    $\displaystyle
    \frac{log 13}{log x} = 10
    $

    Is that the right start?
    $\displaystyle 13^{-x}=10 \Rightarrow 13^x = \frac{1}{10} \Rightarrow (13^x)^2 \frac{1}{100}$ ....
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