Logarithm Calculator

A logarithm answers “what power gives this number?”: log₁₀ 1000 = 3 because 10³ = 1000. Logarithms appear in finance, science, sound (decibels) and computing.

Use 2.718281828 for natural log, or see ln below.
Results update as you type.

log base 10 of 1,000

3

because 10^3 = 1,000

Natural log (ln)
6.907755279
Common log (log₁₀)
3
Binary log (log₂)
9.9657842847

About this calculator

Enter the number and the base.

How to use it

  1. Enter the number.
  2. Enter the base.
  3. Read the logarithms.

The formula

log_b(x) = ln(x) ÷ ln(b)
ln
natural log, base e ≈ 2.718
log
common log, base 10

Worked example

log base 10 of 1000

  1. 10³ = 1000, so the answer is 3.
  2. ln 1000 = 6.908 and log₂ 1000 = 9.966.

What the result means

The antilog is the reverse: 10³ = 1000.

Assumptions

  • Positive numbers and bases, base not 1.

Limitations

  • Logarithms of zero or negatives are undefined for real numbers.

Frequently asked questions

What is log 100?

2, in base 10.

What is ln 1?

0.

How do I change the base?

Divide ln of the number by ln of the base.

Last reviewed on 3 October 2026. Found a mistake? Tell us.