CalcVind

Log Calculator (Logarithm)

Logarithm of any number in any base

Logarithm

Logarithm

3log(1,000)
3
log₁₀
6.90775527898
ln
9.96578428466
log₂

Change of base

  1. log_10(1,000) = ln(1,000) ÷ ln(10)
  2. = 6.90775527898 ÷ 2.30258509299 = 3
  3. Check: 10^3 = 1,000
  1. 1
    Choose a base
    10, e, 2 or any other
  2. 2
    Enter the number
    Or the log, to find the antilog
  3. 3
    Get the answer
    With change-of-base working

What is a logarithm?

A logarithm answers “what power do I raise the base to, to get this number?”

log_b(x) = y ⇔ b^y = x

Change of base: log_b(x) = ln(x) ÷ ln(b)

log(a × c) = log a + log c

log(aⁿ) = n × log a

Common and natural logs

“log” on most calculators means base 10, used for decibels, pH and the Richter scale. “ln” is the natural log with base e ≈ 2.71828, used for growth, decay and compound interest. Base 2 is common in computing.

Why log of 0 or a negative is undefined

No power of a positive base can give 0 or a negative number, so their logarithms don't exist as real numbers.

Related calculators

Frequently asked questions

What is log 1000?

3, because 10³ = 1,000.

What is the difference between log and ln?

log usually means base 10; ln is the natural logarithm, base e ≈ 2.71828. ln(x) = log(x) × 2.302585.

How do I find an antilog?

Raise the base to the logarithm. The antilog of 2.5 in base 10 is 10^2.5 ≈ 316.23. Choose “the number (antilog)” above.

Last reviewed: October 2026