MongoDB $log10 Operator

What Is $log10?

$log10 is a MongoDB aggregation expression that returns the base-10 logarithm of a number. Example: log10(100) = 2 because 10² = 100. It is a shortcut for { $log: [ number, 10 ] }.

$log10 = logarithm base 10

{ $log10: <number> }

// same as:
{ $log: [ <number>, 10 ] }

number → non-negative
result → double (usually)

{ $log10: 1 }     →  0
{ $log10: 10 }    →  1
{ $log10: 100 }   →  2
{ $log10: 1000 }  →  3

null / missing → null
NaN → NaN

How to Use $log10 in MongoDB

Pass one number expression, then store the result in a stage.

1. Choose an expression stage ($addFields or $project).
2. Write { $log10: "$value" }.
3. Confirm the number is non-negative.
4. Use the result for scaling, orders of magnitude, or formulas like pH.

Pseudocode

for each document:
    n = evaluate(numberExpression)
    if n is null or missing:
        result = null
    else if n is NaN:
        result = NaN
    else:
        result = log10(n)   // base-10 logarithm
    emit { ..., field: result }

Cheat Sheet

Keep these facts handy while computing base-10 logs.

Live Preview

Watch $log10 return the base-10 logarithm for common powers of 10.

number = 100

$log10 → 2

Check: 10^2 = 100 ✓

{ result: 2 }

Worked Walkthrough — log₁₀(100)

A reading stores value: 100. We want the base-10 logarithm.

Document:
  { value: 100 }

$log10: "$value"

Ask: 10 to what power equals 100?
  10^2 = 100

Result:
  2

Same as: { $log: [ 100, 10 ] } → 2 ✓

MongoDB Examples

We use one sample document. First we store it, then we compute $log10, then we use it in a simple pH-style formula. Run these in mongosh after inserting the sample data once.

db.samples.insertOne({
  _id: 1,
  label: "Scale",
  value: 100,
  H3O: 0.001
});

db.samples.find()

{
  _id: 1,
  label: "Scale",
  value: 100,
  H3O: 0.001
}

100    --$log10-->  2        (10^2 = 100)
0.001  --$log10--> -3
                   then × -1 → pH 3

db.samples.aggregate([
  {
    $addFields: {
      log10: { $log10: "$value" }
    }
  }
]);

{
  _id: 1,
  label: "Scale",
  value: 100,
  H3O: 0.001,
  log10: 2
}

db.samples.aggregate([
  {
    $project: {
      H3O: 1,
      pH: {
        $multiply: [
          -1,
          { $log10: "$H3O" }
        ]
      }
    }
  }
]);

{
  _id: 1,
  H3O: 0.001,
  pH: 3
}

Performance Notes

Base-10 log is inexpensive compared with large sorts or joins. Filter early with $match when only some documents need the field.

Key Takeaways