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Thread: Can't get to the same result as lecturer

  1. #1
    Junior Member
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    Can't get to the same result as lecturer

    Dear members,
    I was watching the video linked below on fractional dimension. At 2mn I can't get to the final expression for x in terms of y, and how the i exponent disappears :

    $\displaystyle y = \frac{1}{3^i} , x=3*4^i , x = 3*\left (\frac{1}{y} \right )^\frac{\log 4}{\log3}$

    As a starting point I tried to use the x equation and substract y, or multiply by y but it did not get me to the result.

    Thank you very much for your help !

    https://youtu.be/XjKbhgFSuEo?t=2m


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  2. #2
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    Re: Can't get to the same result as lecturer

    $$3^i = e^{\log 3^i} = e^{i \log 3}$$

    $$4^i = e^{\log 4^i} = e^{i\log 4}$$

    $$y = \dfrac{1}{3^i} \Longrightarrow 3^i = \dfrac{1}{y}$$

    From the first equation, we have

    $$e^{i \log 3} = \dfrac{1}{y}$$

    Taking both sides to the power of $\dfrac{\log 4}{\log 3}$ gives:

    $$e^{i\log 4} = \left(\dfrac{1}{y}\right)^{\tfrac{\log 4}{\log 3}}$$

    $$4^i = \left(\dfrac{1}{y}\right)^{\tfrac{\log 4}{\log 3}}$$

    $$3\cdot 4^i = 3\left(\dfrac{1}{y}\right)^{\tfrac{\log 4}{\log 3}}$$

    $$x = 3\left(\dfrac{1}{y}\right)^{\tfrac{\log 4}{\log 3}}$$
    Thanks from topsquark and HallsofIvy
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  3. #3
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    Re: Can't get to the same result as lecturer

    Thank you very much ! :-)
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