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I want to understand how to derive the formula of magnitude error ($\sigma_m$) which is caused by peculiar velocity of a galaxy, like this $$ \sigma_m = \frac{5\ \sigma_V}{cz\ \rm{ln(10)}} $$ ,where $\sigma_V$ is a peculiar velocity and $cz$ is a recession velocity of a galaxy. Could you please tell me the derivation step by step?

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