Logarithm Calculator
Compute logarithms in any base.
Logarithm Calculator
Enter a positive value and a base (use "e" for the natural logarithm), then select Calculate.
How this is calculated
A logarithm answers "to what power must the base be raised to get this value?" Computed via the change-of-base identity: log_b(x) = ln(x) ⁄ ln(b)
Examples
log₁₀(100) = 2, since 10² = 100. log₂(8) = 3, since 2³ = 8. ln(e³) = 3, since the natural logarithm (base e) is the inverse of eˣ.
About this calculation
This uses the standard change-of-base logarithm identity, valid for any positive base other than 1, and any positive value.
Frequently asked questions
What does "e" mean in the base field?
It stands for Euler's number (≈2.71828), giving the natural logarithm (usually written ln). You can also enter any positive number, like 10 (the common logarithm) or 2 (the binary logarithm).
Why does the calculator say my input is invalid?
The value must be a positive number (logarithms of zero or negative numbers aren't defined), and the base must be a positive number other than 1.
Logarithm Solution
log_b(x)
Result will appear here.
Calculation steps