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Derivation of Pogson's law

  1. Feb 3, 2012 #1
    Hello i am strugling to derive Pogson's law, i feel i am soo close, but i am not there yet. Here is what i ve done soo far.


    \begin{equation}
    \begin{split}
    j_6 \cdot 100 &= j_1\\
    \frac{j_6}{j_1} &= \frac{1}{100}\\
    \frac{j_6}{j_1} &= 10^{(-2)}\\
    \frac{j_6}{j_1} &= 10^{-0,4\cdot 5}\\
    \frac{j_6}{j_1} &= 10^{-0,4\cdot (m_6 - m_1)}\\
    \frac{j_1}{j_2} &= 10^{-0,4\cdot (m_1 - m_2) }\\
    \frac{j_1}{j_2} &= 10^{-0,4\cdot (m_1 - m_2) }\\
    \frac{j_1}{j_2} &= 2,5^{-(m_1 - m_2) }\\
    \log_{10} \frac{j_1}{j_2} &= \log_{10} 2,5^{-(m_1 - m_2) }\\
    \log_{10} \frac{j_1}{j_2} &= -(m_1 - m_2) \cdot \log_{10} 2,5\\
    (m_1 - m_2) &= -\frac{\log_{10} \frac{j_1}{j_2}}{\log_{10} 2,5}\\
    \end{split}
    \end{equation}

    What am i missing???
     
  2. jcsd
  3. Feb 3, 2012 #2
    I allready got it. TY
     
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