# What is 5 in 5log10 the value of?

I know what 2.5 stand for in $$2.5 \log_{10}$$, but what does the number 5 in $$5\log_{10}$$ stand for and what application does it have.

Thus, why is the number a five and not a four, or a three, or something else?

2.5 stands for the logarithmic step in apparent magnitude. There must be something similar for the 5 in 5log10. Does it stand for the logarithmic step in absolute magnitude?

• Check the definition of magnitudes and the distance modulus. 5 stands for the number 5. Nov 9, 2021 at 15:08
• I’m voting to close this question because it belongs on Mathematics SE. Nov 9, 2021 at 15:12
• You need to provide details about where these calculations are used. Usually, an equation is something = 5Log10(of something else). What are "something" and "something else"? As presented, 2.5 and 5 are multipliers. That is all we can say without knowing the full context. Nov 9, 2021 at 15:34
• Assuming it refers to the linked posting: It's an empirical formula and 5 stands for the number 5 which happens to match whatever relation is explained in the study it comes from. Nov 9, 2021 at 19:20
• The relation between flux and magnitude is defined (5 magnitudes is a factor of 100 in brightness) and does not follow from anything physical. Nov 10, 2021 at 8:06

A magnitude is defined as $$-2.5\log_{10}$$ of a flux. But flux scales as the inverse square of a distance.
$$-2.5\log_{10}\left(\frac{k}{d^2}\right) = 5\log_{10}(d) -2.5\log_{10}(k)$$