basic

Logarithm Change-of-Base Calculator

log_b(x) = ln(x) / ln(b) = log₁₀(x) / log₁₀(b).

Compute the logarithm of x with respect to an arbitrary base b using the change-of-base identity log_b(x) = ln(x) / ln(b). Particularly useful for bases (2, 3, 7, …) for which calculators lack a dedicated key. Reports log_b(x), the natural log ln(x), and the common log log₁₀(x) for cross-reference.

Daniel Oh By Daniel Oh
Published Last reviewed 1 min read

Inputs

Results

Enter values and click Calculate to see results.
Was this helpful?

How to use this calculator

  1. Fill in the inputs above using the units you already have.
  2. Values update automatically as you type — no submit button needed.
  3. Hover any result row for the underlying formula and intermediate values.

Formula

log_b(x) = ln(x) / ln(b).

In depth

Compute the logarithm of x with respect to an arbitrary base b using the change-of-base identity log_b(x) = ln(x) / ln(b). Particularly useful for bases (2, 3, 7, …) for which calculators lack a dedicated key. Reports log_b(x), the natural log ln(x), and the common log log₁₀(x) for cross-reference.