Log Calculator
Log calculator: find the logarithm of a number for any base, plus the common log and natural log.
Editorial review: Farrow (pseudonym; identity and professional credentials are not disclosed). This page is for educational purposes, not professional advice.
Updated
Your inputs
Results update as you type. Nothing you enter leaves your device.
Results
- Common log (base 10)
- 3
- Natural log (ln)
- 6.90775528
- Binary log (base 2)
- 9.96578428
Example with the starting values
These results use the calculator's initial inputs. Change the values above to calculate your own estimate.
Inputs
- Number
- 1000
- Base
- 10
Results
- log base 10
- 3
- Common log (base 10)
- 3
- Natural log (ln)
- 6.90775528
- Binary log (base 2)
- 9.96578428
How does the Log Calculator work?
The logarithm log_b(x) is the power you raise b to in order to get x. It is computed with the change-of-base formula, ln(x) divided by ln(b).
The base must be positive and not equal to 1, and x must be positive.
Frequently asked questions
What is log base 10 of 1000?
3, because 10 to the power of 3 is 1000.
What is the difference between log and ln?
Log usually means base 10; ln is the natural log with base e, about 2.718.
Why can't I take the log of a negative?
No real power of a positive base gives a negative number.
What is the change of base formula?
log_b(x) = ln(x) / ln(b). It lets you compute any base with a calculator that has only ln or log.