Logarithm Calculator

Enter a number and a base and the logarithm is calculated instantly as you type, with your choice of rounding precision. Prefer a printable reference instead? Browse the logarithm tables.

Logarithm Calculator

Enter the values below — the result updates automatically.

Number (x)

Number to calculate log for

Base (b)

Rounding

Logarithm (y)

Logarithm result

Essentially, this is how you can express the above computation:

$log base b of x equals y$

How Do You Calculate a Logarithm?

A logarithm answers "what power do I raise the base to, to get this number?" The logarithm of x to base b — written log_b(x) — is the exponent y that makes b^y equal x. It's the inverse of exponentiation, the same way subtraction is the inverse of addition.

What does log_b(x) = y actually mean?

It means these two statements are equivalent:

$log base b of x equals y, which is equivalent to b to the power y equals x$

For example, log₂(8) = 3, because 2³ = 8. In simple, whole-number cases like that one, the logarithm is really just counting how many times you multiply the base by itself to reach the number.

Which base should I use?

Base 10 (the calculator's default) is the most common for everyday use and scientific notation. Base 2 shows up constantly in computing (doubling, binary). Base e (Euler's number, ≈2.71828) is the natural logarithm, ln(x) — the one calculus and most growth/decay formulas actually use. This calculator works with any base you enter.