Logarithm Calculator

Calculate logarithms with different bases including natural logarithm (ln) and common logarithm (log₁₀). Enter your number and select a base to get instant results.

Number (must be positive)

Base (must be positive, not equal to 1)

How to Use

Enter a Number: Input any positive number you want to calculate the logarithm for
Choose a Base: Enter a custom base or use the quick options for natural log (e ≈ 2.71828) or common log (10)
Quick Options: Click "Natural Log" for ln(x) or "Common Log" for log₁₀(x)
Calculate: Click the calculate button to see your result

What is a Logarithm?

A logarithm is the inverse operation of exponentiation. The logarithm of a number is the exponent to which the base must be raised to produce that number. For example, log₁₀(100) = 2 because 10² = 100.

Common Logarithm Types

Natural Logarithm (ln): Uses base e (approximately 2.71828), widely used in mathematics and science
Common Logarithm (log): Uses base 10, commonly used in engineering and pH calculations
Binary Logarithm (log₂): Uses base 2, frequently used in computer science
Custom Base: Any positive number (except 1) can be used as a base

Important Notes

The number must be positive (greater than 0)
The base must be positive and not equal to 1
Logarithms of negative numbers and zero are undefined in real numbers
log_b(1) always equals 0 for any valid base b
log_b(b) always equals 1 for any valid base b