What Steps Are Missing in Deriving Pogson's Law?

[71GA]

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?

 

[71GA]

I allready got it. TY