# log10

Learn how to use the log10 function in Notion formulas.
The log10() function returns the base-10 logarithm of a number.
1
log10(number)
For reference, here are the named components of a logarithm:
$\log_{base} argument = exponent$
A logarithm is the exponent of the base that returns the argument.

## Example Formulas

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log10(1000) // Output: 3
2
3
log10(10) // Output: 1
Want to learn more about logarithms? Check out this resource:

### Computing Logs with Other Bases (Log Base X)

Notion only provides log10(), log2, and ln because those are by far the most commonly-used log bases.
However, if you need to compute a log with a different base, you can use the change of base formula:
$\log_x y= (\frac{\ln y}{\ln x})$
So, for example:
$\log_3 81 = (\frac{\ln 81}{\ln 3})$
Here’s a Notion formula to compute this:
1
ln(81) / ln(3) // Output: 4

## Example Database

$log_{10}$
can be used to perform an interesting mathematical trick – finding the length (i.e. number of digits) in any number. It is done by taking the floor value of a number’s
$log_{10}$
, then adding one:
$\lfloor log_{10}n \rfloor + 1$
The example database below shows this trick in action.

### "Length" Property Formula

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// Compressed
2
floor(log10(prop("Num"))) + 1
3
4
// Expanded
5
floor(
6
log10(
7
prop("Num")
8
)
9
) + 1
If you’re curious about the math behind why this trick works, check out this thread:
The formula itself is quite simple:
1. 1.
We pass prop("Num") to the log10() function.
2. 2.
This value is then run through the floor function in order to round it to its nearest integer of lower or equal value.
3. 3.
Finally, we add 1.

#### About the Author

My name is Thomas Frank, and I'm a Notion-certified writer, YouTuber, and template creator. I've been using Notion since 2018 to organize my personal life and to run my business and YouTube channel. In addition to this formula reference, I've created a free Notion course for beginners and several productivity-focused Notion templates. If you'd like to connect, follow me on Twitter.