# log2

Learn how to use the log2 function in Notion formulas.

1

log2(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.1

log2(64) // Output: 6

2

3

log2(2) // Output: 1

Want to learn more about logarithms? Check out this resource:

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

$log_{2}$

can be used to perform an interesting mathematical trick – finding the length (i.e. number of digits) in any number **when represented in binary**. It is done by taking the**floor value**of a number’s$log_{2}$

, then adding one:$\lfloor log_{2}n \rfloor + 1$

The example database below shows this trick in action. Unfortunately, actual binary representation of a base-10 number in Notion is not possible (or at least has not been solved by the Notion community), but you can check the result using this converter.

1

// Compressed

2

floor(log2(prop("Num"))) + 1

3

4

// Expanded

5

floor(

6

log2(

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.We pass
`prop("Num")`

to the`log10()`

function. - 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.Finally, we add
`1`

.

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.

Last modified 4mo ago