Logarithm Calculator
Calculate the natural logarithm or a logarithm to a chosen base (log, ln).
Tip: log₁₀ (the common logarithm) and ln (the natural logarithm, base e) are the most used.
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About this digital tool
The logarithm calculator finds the logarithm of a positive number to any base you choose, and also shows the natural logarithm ln. Enter the number and the base (10 by default) and get the result instantly. The number must be positive and the base positive and not equal to 1.
The logarithm of a number to base b is the power to which b must be raised to get the number. So log₁₀(100) = 2 because 10² = 100, and log₂(8) = 3 because 2³ = 8. For other bases the change-of-base formula is used: logb(x) = ln(x) ÷ ln(b). Logarithms are used for the Richter and decibel scales, for pH in chemistry, for compound interest and in computer science.
How to use
- Enter the positive number whose logarithm you want.
- Enter the base (10 for the common log, 2 for binary, or any positive value ≠ 1).
- Read the logarithm in the result bar.
- Also see ln, the natural logarithm with base e, if you need it.
Frequently asked questions
What is the difference between log and ln?
log (with no base) usually means base 10. ln is the natural logarithm with base e ≈ 2.71828. In programming, log often means ln.
How do I calculate a logarithm with a base other than 10?
Use the formula logb(x) = ln(x) ÷ ln(b). E.g. log₂(8) = ln(8) ÷ ln(2) = 2.0794 ÷ 0.6931 = 3. Or enter base 2 directly in the calculator.
Why is there no logarithm of negative numbers or zero?
Because no real power of a positive base gives a negative number or zero. That is why the calculator requires a number greater than 0.
What are log(1) and the log of the base itself?
log(1) is always 0, because any base to the power 0 gives 1. And logb(b) = 1, e.g. log₁₀(10) = 1.