Logarithm Calculator (log, ln, antilog)
Find the logarithm of any number in base 10, base e (ln), base 2 or a base of your choice, or work back from a log to the number with the antilog.
log₁₀(1,000)
3
- ln(1,000)
- 6.907755279
- log₂(1,000)
- 9.9657842847
log₁₀(1,000) = 3: raising 10 to the power 3 gives 1,000.
How it's worked out
- Change of base
ln 1,000 ÷ ln 10 = 6.90775528 ÷ 2.302585093 - Check
10^31,000
The rules
log_b(x) = y means bʸ = x · log_b(x) = ln x ÷ ln b
log(xy) = log x + log y · log(x ÷ y) = log x − log y · log(xⁿ) = n log x
Examples
log₁₀(1000) = 3 · log₂(8) = 3 · ln(e) = 1 · log₅(125) = 3 · antilog₁₀(2) = 100
Questions people ask
What is a logarithm?
The power you raise the base to in order to get the number. log₁₀(1000) is 3 because 10³ = 1000.
What is the difference between log and ln?
log usually means base 10 and ln means base e (about 2.71828), the natural logarithm. ln(10) is about 2.302585.
How do I find a log in another base?
Use the change-of-base rule: log_b(x) = ln(x) ÷ ln(b). So log₅(125) = ln 125 ÷ ln 5 = 3.
What is an antilog?
The reverse of a log: the base raised to the power. The antilog of 2 in base 10 is 10² = 100.
Why can't I take the log of zero or a negative number?
No power of a positive base gives zero or a negative number, so the logarithm isn't defined there.
About this calculator
Formula and rules last checked 26 October 2026Written and tested by the CalculatorDex teamReport a problem