Math

Logarithm Calculator

Evaluate logarithms quickly with support for log base 10, natural log (ln), and any custom base you specify.

logarithmlog base 10natural log

Logarithms

Evaluate logs in base 10, e, or any custom base.

ArgumentBaseCustom base

log₍base₎(argument)

log₁₀(argument)

2.40823997

ln(argument)

5.54517744

Change of base

log_b(a) = ln(a) ÷ ln(b)

The calculator uses the change-of-base identity to evaluate any base with high precision, showing both natural and base-10 equivalents.

Enter the argument (a) you want the log of.
Select base 10, e, or type a custom base.
Read the logarithm value with up to eight decimal places and copy-friendly formatting.

Example

Input: Argument = 256, Base = 2

Output: log₂(256) = 8

Can I log negative numbers?

Real logarithms only accept positive arguments. The calculator flags invalid inputs if the argument or base is non-positive.

Does it show natural logs too?

Yes—the results panel includes both log₁₀ and ln so you can compare values instantly.