Logarithm Calculator
Calculate log base 10, natural log (ln), binary log, or any custom base instantly — with step-by-step working.
Calculate Logarithm
log₁₀(x)
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Step-by-Step
Enter a number and select a base to see the working.
Formula (change of base)
Substitute Values
Compute
Verification
Common Logarithm Values
| x | log₁₀(x) | ln(x) | log₂(x) |
|---|
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Summary
Calculate log base 10, natural log (ln), binary log, or any custom base instantly — with step-by-step working.
How it works
- Enter the number (x) you want to find the logarithm of.
- Select a preset base — log₁₀, ln (base e), log₂ — or type any custom positive base.
- The result appears instantly as you type.
- The step-by-step panel shows the change-of-base formula applied to your inputs.
- Use the inverse field to verify: raise the base to the result and confirm you recover x.
Use cases
- Solve algebra and pre-calculus homework involving logarithms.
- Convert between logarithm bases using the change-of-base formula.
- Compute decibel levels or Richter magnitude (base-10 log).
- Work with information theory and entropy calculations (base-2 log).
- Check natural-log values for calculus derivatives and integrals.
- Verify logarithm identities: log_b(x*y) = log_b(x) + log_b(y).
- Find exponents: if b^n = x, compute n = log_b(x).
- Science and engineering: pH, stellar magnitude, bit depth analysis.
Frequently Asked Questions
Last updated: 2026-06-10 ·
Reviewed by Nham Vu