Log Calculator (Logarithm)

Welcome to our logarithm calculator! Whether you're a student tackling complex math problems, a scientist working with exponential data, or just curious about logarithms, our tool is designed to make your calculations quick and accurate.

What are Logarithms?

Logarithms are the inverse operations to exponents. They answer the question: to what power must a given number (the base) be raised to produce another number? For example, log10(100) = 2, because 102 = 100.

How to Use Our Calculator

  1. Enter the number you want to find the logarithm of in the "Number" field.
  2. Specify the base in the "Base" field. Use 10 for common logs, 'e' for natural logs, or any positive number.
  3. Choose whether to round the result and set the number of decimal places.
  4. Click "Calculate" to see your result!
Enter a number or "e" for natural logarithm

Common Logarithms ℹ️Click on a button to automatically fill in the calculator

Why Use Our Log Calculator?

  • Versatile: Compute logarithms with any base, including natural logs (base e).
  • Precise: Get results up to 15 decimal places for high accuracy.
  • User-friendly: Intuitive interface with helpful tooltips and quick-select buttons.
  • Educational: Understand logarithms better with our clear explanations and examples.

Whether you're solving exponential equations, working with pH levels in chemistry, or analyzing financial growth rates, our logarithm calculator is your go-to tool for quick and reliable results.

How to Use the Logarithm Calculator: A Step-by-Step Guide

Steps to Calculate a Logarithm

  1. Enter the number you want to find the logarithm of in the "Number" field.
  2. Specify the base in the "Base" field (use 10 for common logs, 'e' for natural logs, or any positive number).
  3. Choose whether to round the result and set the number of decimal places.
  4. Click "Calculate" to see your result!

Logarithm Examples

Common Logarithm (Base 10)

Example: log10(100)

  • Number: 100
  • Base: 10
  • Result: 2

Explanation: 102 = 100, so log10(100) = 2

Natural Logarithm (Base e)

Example: ln(e3) or loge(e3)

  • Number: 20.0855...
  • Base: e
  • Result: 3

Explanation: e3 ≈ 20.0855, so ln(20.0855) = 3

Binary Logarithm (Base 2)

Example: log2(32)

  • Number: 32
  • Base: 2
  • Result: 5

Explanation: 25 = 32, so log2(32) = 5

Custom Base Logarithm

Example: log3(81)

  • Number: 81
  • Base: 3
  • Result: 4

Explanation: 34 = 81, so log3(81) = 4

Practical Applications of Logarithms