MongoDB $log10 Operator

What You’ll Learn

The $log10 operator calculates the base-10 logarithm of a number in an aggregation expression. It is a convenient shortcut when you need common logarithms — the same as { $log: [ number, 10 ] } but simpler to write.

Definition and Usage

In MongoDB’s aggregation framework, the $log10 operator computes log₁₀(number) — the power you must raise 10 to in order to get the number. For example, log₁₀(100) = 2 because 10² = 100, and log₁₀(1000) = 3 because 10³ = 1000.

Think of $log10 as MongoDB’s pipeline version of JavaScript’s Math.log10(). When you only need base 10, it is cleaner than writing { $log: [ "$value", 10 ] }.

📝 Syntax

The $log10 operator takes one numeric expression:

{ $log10: <expression> }

Common Patterns

// Field reference
{ $log10: "$value" }

// Literal number
{ $log10: 100 }

// Equivalent $log form
{ $log: [ "$value", 10 ] }

Syntax Rules

• $log10 — returns the base-10 logarithm of the expression.
• <expression> — must evaluate to a positive number for a valid result.
• log₁₀(1) = 0 — the log of 1 is always zero.
• null input — returns null.
• Use inside stages like $project, $addFields, or $set.
• Equivalent to { $log: [ number, 10 ] } when base is always 10.

Examples Gallery

Walk through a data collection with large numeric values and compute base-10 logarithms step by step.

[
  { "_id": ObjectId("609c26812e9274a86871bc6a"), "label": "Small", "value": 100 },
  { "_id": ObjectId("609c26812e9274a86871bc6b"), "label": "Medium", "value": 1000 },
  { "_id": ObjectId("609c26812e9274a86871bc6c"), "label": "Large", "value": 10000 }
]

db.data.aggregate([
  {
    $project: {
      label: 1,
      value: 1,
      log10Value: { $log10: "$value" }
    }
  }
])

{ "_id": ObjectId("609c26812e9274a86871bc6a"), "label": "Small",  "value": 100,   "log10Value": 2 }
{ "_id": ObjectId("609c26812e9274a86871bc6b"), "label": "Medium", "value": 1000,  "log10Value": 3 }
{ "_id": ObjectId("609c26812e9274a86871bc6c"), "label": "Large",  "value": 10000, "log10Value": 4 }

db.data.aggregate([
  {
    $project: {
      label: 1,
      value: 1,
      logScale: { $log10: "$value" },
      magnitude: {
        $floor: { $log10: "$value" }
      }
    }
  }
])

// Small  (100)   → logScale: 2,     magnitude: 2
// Medium (1000)  → logScale: 3,     magnitude: 3
// Large  (10000) → logScale: 4,     magnitude: 4

db.data.aggregate([
  {
    $project: {
      label: 1,
      value: 1,
      viaLog10: { $log10: "$value" },
      viaLog: {
        $log: [ "$value", 10 ]
      }
    }
  }
])

// viaLog10 and viaLog are identical for every document
// e.g. value 1000 → both return 3

db.data.aggregate([
  {
    $project: {
      label: 1,
      value: 1,
      safeLog10: {
        $cond: [
          { $gt: [ "$value", 0 ] },
          { $log10: "$value" },
          null
        ]
      }
    }
  }
])

db.sensors.aggregate([
  {
    $project: {
      sensor: 1,
      powerRatio: 1,
      dB: {
        $multiply: [
          10,
          { $log10: "$powerRatio" }
        ]
      }
    }
  }
])

// powerRatio 100 → dB: 20  (10 × log10(100) = 10 × 2)

🚀 Use Cases

• Scaling data — compress large values spanning many orders of magnitude onto a readable log scale.
• Decibel calculations — acoustics, electronics, and signal processing often use base-10 logs.
• Data transformation — normalize skewed distributions before statistical analysis.
• Order of magnitude — bucket or label values by their power-of-10 range.

💡 Best Practices