Find the logarithm of a number in any base — plus natural log, log base 10 and log base 2.
Understanding the log calculation
Enter a value and a base and this calculator returns the logarithm, along with the common natural, base-10 and base-2 logs.
Logs answer “what power do I raise the base to, to get this number?”
Step by step
- Enter the value.
- Enter the base (10, e-equivalent, 2 or any positive number).
- Read the logarithm and common logs.
How the number is calculated
logₘ(x) = ln(x) ÷ ln(base)
Try it with these numbers
On the values this calculator opens with, the logᵇ(x) is 3. Underneath, Natural log comes out at 6.9078 and Log base 10 at 3. Change any field and every figure updates as you type.
Questions people ask about this
What is a logarithm?
The inverse of exponentiation. log base 10 of 1000 is 3, because 10³ = 1000.
What’s the natural log?
Log to the base e (about 2.718), written ln. It appears throughout science and finance.
Why does base matter?
Different bases answer the same question relative to a different starting number. Base 2 is common in computing, base 10 in everyday math.