Logarithm Change of Base Calculator
Compute log base b of x using the change-of-base formula.
Enter your values
ⓘ Live results
Results
- log_b(x)
- 2.861353
- ln(x)
- 4.60517
- ln(b)
- 1.609438
Quick answer
log_b(x) = ln(x)/ln(b), letting you compute a logarithm in any base using natural or common logs.
log_b(x) = ln(x)/ln(b)
How to use the Logarithm Change of Base Calculator
- 1Enter the value x whose logarithm you want.
- 2Enter the base b you want the logarithm expressed in.
- 3The change-of-base formula divides ln(x) by ln(b) to get log_b(x).
Worked example
Using the values the calculator loads with:
Inputs
- Value x100
- Base b5
Results
- log_b(x)2.861353
- ln(x)4.60517
- ln(b)1.609438
Frequently asked questions
Why can't the base be 1?
log base 1 is undefined since 1 raised to any power is always 1.
Does this work for base 2?
Yes — any positive base other than 1 works, including base 2 for binary logarithms.
About this calculator
- Built and reviewed by James Whitfield · How we build and test calculators
- Report an error
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.