MultiConvers

Log Calculator

Choose common log (base 10), natural log (base e), binary log (base 2), or type a custom base, then enter the number.

How it works

A logarithm answers “what power of this base gives the number?” log₁₀(1000) = 3 because 10³ = 1000. Change of base is the working identity: log_b(x) = ln(x) / ln(b). The number must be positive.

The base must be positive and not 1 — log base 1 is undefined, and logs of zero or negatives are not real. Those cases are rejected instead of printing −Infinity or NaN.

Formula

log_b(x) = ln(x) / ln(b)
log₁₀(1000) = 3
ln(e) = 1
log₂(8) = 3

Worked examples

  • Common log

    log₁₀(1000) → 3

  • Binary log

    log₂(8) → 3

Useful notes

  • On the scientific calculator, log is also base 10 and ln is natural log.
  • The inverse of a logarithm is exponentiation — use the exponent calculator to check.

FAQ

What is the difference between log and ln?

On this page, common log is base 10 and ln is base e ≈ 2.71828. Both are logarithms; only the base changes.

How do I change the base of a logarithm?

Divide natural logs: log_b(x) = ln(x) / ln(b). That is what the custom-base mode does.

Why is log(0) rejected?

There is no real power of a positive base that equals 0. The real logarithm is only defined for positive numbers.

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