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

1. 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

2. 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:

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

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

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

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

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

Thank you very much ! :-)