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Log Calculator: Logarithm in Any Base

This log calculator finds log base 10, ln, log2, or any other positive base except 1. It shows the change-of-base steps and can switch to antilog.

What do you want?

log_b(x) is the exponent that turns b into x. The math stays in your browser.

Base

Must be positive. log10(1000) = 3 because 10^3 = 1000.

Common log, base 10.

Result

3

log₁₀(1,000) = 3

Change of base. ln(1,000) / ln(10) = 6.907755 / 2.302585 = 3

Check. 10^3 = 1,000

How to use

  1. Choose Logarithm or Antilog.
  2. Pick log10, ln, log2, or a custom base. A custom base must be positive and not 1.
  3. Enter the number for a log, or the exponent for an antilog.
  4. Read the result, the change-of-base steps, and the power check. Clear empties the fields.

Formula

log_b(x) = ln(x) / ln(b), which is the same as log10(x) / log10(b). The base must be positive and not 1, and x must be positive. ln is log base e (about 2.71828). log10 is the common log and log2 is the binary log. Antilog_b(y) = b^y.

Example. log₁₀(1,000) = 3 because 10^3 = 1,000. Change of base: ln(1,000) / ln(10) = 6.907755 / 2.302585 = 3. log₂(8) = 3. antilog₁₀(3) = 10^3 = 1,000.

Real numbers only

A logarithm of zero or a negative number is not a real number, so this page rejects those inputs. Bases of 1 and 0 are rejected for the same reason. Very large powers that overflow show an error instead of infinity.

Frequently asked questions

What is a logarithm?

log_b(x) is the exponent you raise b to in order to get x. log10(1000) = 3 because 10^3 = 1000.

What is ln?

The natural logarithm, log base e (about 2.71828).

How do I calculate a log in another base?

Use change of base: log_b(x) = ln(x) / ln(b). log2(8) = ln 8 / ln 2 = 3.

Can you take the log of a negative number?

Not in the real numbers. The logarithm is only defined for positive x.

What is an antilog?

The inverse of a log: antilog_b(y) = b^y.

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