Debug Info:
{
  "title": "Logarithm",
  "symbol": "log",
  "definition": "The logarithm of a number is the exponent to which another fixed value, the base, must be raised to produce that number.",
  "usage": "Used in solving exponential equations, measuring earthquake intensity (Richter scale), and in information theory.",
  "examples": [
    {
      "description": "Natural logarithm",
      "latex": "\\ln(x) = y \\iff e^y = x"
    },
    {
      "description": "Logarithm with base 10",
      "latex": "\\log_{10}(100) = 2"
    }
  ],
  "tags": [
    "algebra",
    "analysis",
    "functions"
  ],
  "relatedConcepts": [
    "exponential function",
    "change of base formula",
    "logarithmic scale"
  ]
}

Logarithm

Symbol

log

Definition

The logarithm of a number is the exponent to which another fixed value, the base, must be raised to produce that number.

Usage

Used in solving exponential equations, measuring earthquake intensity (Richter scale), and in information theory.

Examples

Description: Natural logarithm

LaTeX: \ln(x) = y \iff e^y = x
Description: Logarithm with base 10

LaTeX: \log_{10}(100) = 2

Tags