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Logarithm Calculator

Calculate logarithms with any base instantly

Calculate Logarithm

Result

Enter values to see the result

About Logarithm Calculator

A logarithm calculator is a powerful mathematical tool that helps you find the logarithm of any positive number with any specified base. The logarithm answers the question: "To what power must the base be raised to get the given number?"

For example, log₁₀(100) = 2 because 10² = 100. This calculator supports:

  • Common Logarithm (log₁₀): Base 10, widely used in science and engineering
  • Natural Logarithm (ln): Base e (≈2.718), essential in calculus and exponential growth
  • Binary Logarithm (log₂): Base 2, important in computer science and information theory
  • Custom Base: Any positive number except 1

How to Use the Logarithm Calculator

Step-by-Step Instructions:

  1. Choose or enter the base (b) for your logarithm
  2. Use quick buttons for common bases: 10, e, or 2
  3. Enter the positive number (x) you want to find the log of
  4. Click "Calculate logb(x)" to get your result
  5. View the detailed result with explanation

Examples:

log₁₀(1000) = 3
Because 10³ = 1000
ln(e²) = 2
Because e² = e²
log₂(8) = 3
Because 2³ = 8

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