Skip to content

Science · free · no sign-up

Log Calculator

Calculate logarithms to base 10, base 2, the natural logarithm (base e) or any custom base.

How it works Report a problem

Log CalculatorLogarithm

Multi-Base Computational Engine

About the Log Calculator

Calculate logarithms to base 10, base 2, the natural logarithm (base e) or any custom base.

How to use the Log Calculator

  1. Enter the Input Value (x), which must be positive.
  2. Choose LOG₁₀, LN(e), LOG₂ or CUSTOM and enter the Base (b) if needed.
  3. Press Calculate.

Formula and method

log_b(x) = y means bʸ = x. Change of base: log_b(x) = ln(x) ÷ ln(b).

Worked example

log₁₀(1,000) = 3, log₂(8) = 3 and ln(e) = 1.

Common logs. log₁₀(1,000) = 3, because 10³ = 1,000. And ln(e) = 1.

When to use the Log Calculator

  • Solving equations where the unknown is an exponent.
  • Working with pH, decibels and earthquake magnitudes.
  • Converting between logarithm bases.

Common mistakes to avoid

  • Trying to take the logarithm of zero or a negative number.
  • Mixing up log (base 10) and ln (base e).

Tips

  • The logarithm of a non-positive number is not defined for real numbers.
  • log(a × b) = log a + log b.

Frequently asked questions

What is a natural logarithm?
A logarithm to base e, where e ≈ 2.71828.
How do I change the base of a logarithm?
log_b(x) = log(x) ÷ log(b), using any base for the two logs on the right.
Why are logarithms useful?
They turn multiplication into addition and let us handle huge ranges of values on a manageable scale.