Logarithm Calculator
Calculate a logarithm with a chosen base and review the change-of-base formula.
Calculate a logarithm
Enter a positive value and a valid base. The calculator supports common base 10 and natural-log relationships through the change-of-base rule. The value must be greater than zero, and the base must be positive and not equal to 1.
Change of base
Log base b of x equals ln(x) divided by ln(b). The same relationship can use another valid logarithm base. Keep the base visible because log without a written base can mean different conventions in different classes.
Worked example
Log base 10 of 1000 is 3. Log base 2 of 8 is 3. Check the domain before interpreting a result.
Frequently asked questions
Frequently Asked Questions About Online Calculators
What is the natural logarithm?
The natural logarithm uses the constant e as its base and is written ln.
Can the base be 1?
No. A logarithm base of 1 is undefined.
Can I use a negative value?
Not for this real-number calculator workflow; the input value must be positive.