Logarithm Calculator (Log and Antilog)
Choose the base, type the number and get its logarithm with the working. Switch to Antilog to go back the other way.
- Nothing you type is stored
- Free
- No signup
Logarithm
3
- Natural log (ln x)
- 6.90775528
- Common log (log₁₀ x)
- 3
- Binary log (log₂ x)
- 9.96578428
Show working
- log₁₀(1000) = ln(1000) ÷ ln(10)
- = 6.907755279 ÷ 2.302585093
- = 3
- 10³ = 1000
How to use
- Choose Logarithm or Antilog.
- Pick the base: 10, e, 2 or Other (type your base).
- Type the number and read the answer, plus ln, log₁₀ and log₂ for comparison.
Good to know
log_b(x) = y means bʸ = x: log₁₀ 1000 = 3 because 10³ = 1000. Any base works through the change-of-base formula log_b(x) = ln x ÷ ln b, which the steps show. ln is the natural log, base e ≈ 2.71828.
Antilog is the reverse: antilog₁₀(2) = 10² = 100. Before calculators, Class 11 students multiplied large numbers with log tables, using log(ab) = log a + log b and log(aⁿ) = n log a. The same rules explain the decibel scale, pH and the Richter scale.
Logarithms exist only for positive numbers, and the base must be positive and not 1. log₁₀ 2 ≈ 0.30103 is handy: it tells you that 2¹⁰ ≈ 10³. Results are accurate to about 10 decimal places; whole-number answers such as log₂ 8 = 3 are shown exactly.
Questions
What is the value of log 2?
log₁₀ 2 ≈ 0.30103, and ln 2 ≈ 0.693147.
What is the difference between log and ln?
log usually means base 10 (common log); ln is base e (natural log). ln x = 2.302585 × log₁₀ x.
How do I find log with a different base?
Use log_b(x) = log x ÷ log b. log₅ 125 = log 125 ÷ log 5 = 2.0969 ÷ 0.69897 = 3.
What is antilog?
The inverse of log. If log x = 1.5, then x = antilog 1.5 = 10^1.5 ≈ 31.62.
Why can't I take the log of 0 or a negative number?
No power of a positive base gives 0 or a negative number, so the log is not defined there.