MongoDB $ln Operator

What Is $ln?

$ln is a MongoDB aggregation expression that returns the natural logarithm of a number—log base e (about 2.71828). The input must be a positive number.

$ln = Math.log for aggregation (base e)

{ $ln: <expression> }

ln(1) → 0
ln(e) → 1
input → must be > 0

null / missing → null
0 or negative → error

inverse → $exp

How to Use $ln in MongoDB

Pass a positive number expression and emit the natural log.

1. Choose an expression stage ($addFields or $project).
2. Confirm the value is greater than 0 (filter or validate first if needed).
3. Pass the field or expression to $ln.
4. Use $exp when you need the inverse.

Pseudocode

for each document:
    x = evaluate(expression)
    if x is null or missing:
        result = null
    else if x <= 0:
        error  // natural log undefined
    else:
        result = ln(x)   // base e
    emit { ..., field: result }

Cheat Sheet

Keep these facts handy while using natural logs in pipelines.

Live Preview

Watch $ln on common positive values. Zero and negatives are invalid.

value = 2.718281828459045 (e)

$ln → 1

{ naturalLog: 1 }

Worked Walkthrough — ln(e)

A sample stores e (about 2.718). The natural log of e is exactly 1—the cleanest check that $ln is working.

Document:
  { label: "unit-e", value: Math.E }   // ≈ 2.71828

$ln("$value")
  = ln(e)
  ≈ 1

Handy checks:
  ln(1) = 0
  ln(e) = 1
  $exp(1) ≈ e   // inverse

MongoDB Examples

We use one sample value equal to Math.E. First insert it, then compute $ln, then show ln(1) beside it. Run these in mongosh after inserting the sample data once.

db.samples.insertOne({
  _id: 1,
  label: "unit-e",
  value: Math.E
});

db.samples.find()

{
  _id: 1,
  label: "unit-e",
  value: 2.718281828459045
}

value ≈ 2.71828  (= e)

$ln(value) → 1

because e¹ = e

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

{
  _id: 1,
  label: "unit-e",
  value: 2.718281828459045,
  naturalLog: 1
}

db.samples.aggregate([
  {
    $addFields: {
      lnOfValue: { $ln: "$value" },
      lnOfOne: { $ln: 1 }
    }
  }
]);

{
  _id: 1,
  label: "unit-e",
  value: 2.718281828459045,
  lnOfValue: 1,
  lnOfOne: 0
}

Performance Notes

Natural log is inexpensive. Filter invalid or unused documents early with $match when only some rows need a log.

Key Takeaways