📉Logarithm Calculator

Calculate logarithms with any base including natural log and log base 10.

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About Logarithm Calculator

Calculate logarithms for any base — common log (base 10), natural log (base e, ln), binary log (base 2), and any custom base. Enter the number and base to see the result, along with the inverse (antilogarithm) and the change-of-base formula breakdown.

How to Use Logarithm Calculator

1
Enter the number
Type the value you want to find the logarithm of (must be positive).
2
Choose the base
Select log₁₀, ln (natural log), log₂, or enter a custom base.
3
Read the result
The logarithm is displayed with the formula and optional antilog result.

Common Use Cases

Solving exponential and logarithmic equations in algebra
Calculating pH values and decibel levels
Computing information entropy in bits (log₂)
Understanding exponential growth and decay problems

Frequently Asked Questions

What is the difference between log and ln?

log (or log₁₀) is the common logarithm with base 10. ln is the natural logarithm with base e (≈2.71828). log₂ is the binary logarithm used in computing. All are related by the change-of-base formula: logₙ(x) = ln(x)/ln(n).

Can I calculate antilogarithms?

Yes — toggle to Antilog mode and enter a logarithmic value to calculate the original number (10^x for base 10, e^x for natural log).