<p>A magnitude is defined as <span class="math-container">$-2.5\log_{10}$</span> of a flux. But flux scales as the inverse square of a distance.</p>
<p><span class="math-container">$$-2.5\log_{10}\left(\frac{k}{d^2}\right) = 5\log_{10}(d) -2.5\log_{10}(k)$$</span></p>

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2021-11-09T23:29:29.913Z
2021-11-10T01:32:33.243Z
2021-11-10T01:32:33.243Z
ProfRob
<p>This appears to be a question directed at an answer to a previous question by the OP. <a href="https://astronomy.stackexchange.com/a/47296/26216">https://astronomy.stackexchange.com/a/47296/26216</a></p>
<p>The 5log_10(...) appears to just be a multiplier the author of the paper cited in the aforementioned answer found to describe the visible magnitude of Neptune. Sorry, but that's probably the best answer you'll get...
There may be something special about its formulation, or it could just be a curve that best fitted the data.</p>

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2021-11-09T15:56:30.200Z
2021-11-09T15:56:30.200Z
BMF
<p>I know what 2.5 stand for in <span class="math-container">$2.5 \log_{10}$</span>, but what does the number 5 in <span class="math-container">$5\log_{10}$</span> stand for and what application does it have.</p>
<p>Thus, why is the number a five and not a four, or a three, or something else?</p>
<p>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?</p>

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2021-11-09T15:08:17.620Z
Check the definition of magnitudes and the distance modulus. 5 stands for the number 5.
AtmosphericPrisonEscape
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2021-11-09T15:12:51.997Z
I’m voting to close this question because it belongs on Mathematics SE.
WarpPrime
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2021-11-09T15:16:36.330Z
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?
Constantthin
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2021-11-09T15:34:39.720Z
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.
JohnHoltz
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2021-11-09T16:02:56.570Z
@JohnHoltz OP is most definitely referring [this](https://astronomy.stackexchange.com/a/47296/26216) answer to their previous question.
BMF
CC BY-SA 4.0
2021-11-09T19:20:34.867Z
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.
planetmaker
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2021-11-10T03:12:22.193Z
@Planetmaker. Usually values in a formula comes from somewhere. Is 2.5 also empirical in 2.5log10 and an accidental match with the step in apparent magnitude? Or does it actually derive from there?
Constantthin
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2021-11-10T08:06:41.017Z
The relation between flux and magnitude is defined (5 magnitudes is a factor of 100 in brightness) and does not follow from anything physical.
planetmaker
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2021-11-14T10:14:12.010Z
@fasterthanlight "because it belongs on..." is still not a close reason. If one wants to close it as off-topic here one explains why it's off-topic here. As there are already two good Astronomy answers **I'm voting to keep open**.
uhoh
<apparent-magnitude><absolute-magnitude>
What is 5 in 5log10 the value of?
Constantthin
# What is 5 in 5log10 the value of?

(Asked by: username_0 on 2021-11-09)

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?

**Tags:** apparent-magnitude, absolute-magnitude

> **Comments:**
> **username_1**: Check the definition of magnitudes and the distance modulus. 5 stands for the number 5.  
> **username_2**: I’m voting to close this question because it belongs on Mathematics SE.  
> **username_0**: 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?  
> **username_3**: 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.  
> **username_4**: @username_3 OP is most definitely referring [this](https://astronomy.stackexchange.com/a/47296/26216) answer to their previous question.  
> **username_5**: 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.  
> **username_0**: @Planetmaker. Usually values in a formula comes from somewhere. Is 2.5 also empirical in 2.5log10 and an accidental match with the step in apparent magnitude? Or does it actually derive from there?  
> **username_5**: The relation between flux and magnitude is defined (5 magnitudes is a factor of 100 in brightness) and does not follow from anything physical.  
> **username_6**: @fasterthanlight "because it belongs on..." is still not a close reason. If one wants to close it as off-topic here one explains why it's off-topic here. As there are already two good Astronomy answers **I'm voting to keep open**.  

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## 2 answers

### Answer by username_7 on 2021-11-09. Score: 4

A magnitude is defined as $-2.5\log\_{10}$ of a flux. But flux scales as the inverse square of a distance.

$$-2.5\log\_{10}\left(\frac{k}{d^2}\right) = 5\log\_{10}(d) -2.5\log\_{10}(k)$$


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### Answer by username_4 on 2021-11-09. Score: 1

This appears to be a question directed at an answer to a previous question by the OP. <https://astronomy.stackexchange.com/a/47296/26216>

The 5log\_10(...) appears to just be a multiplier the author of the paper cited in the aforementioned answer found to describe the visible magnitude of Neptune. Sorry, but that's probably the best answer you'll get...
There may be something special about its formulation, or it could just be a curve that best fitted the data.


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