Logarithm Calculator

What This Calculator Does

A logarithm is the reverse of raising to a power. Powers ask “what is $2^3$?” (the answer is 8); a logarithm asks the opposite: “what power turns 2 into 8?” (the answer is 3, so $\log_2 8 = 3$).

In plain words, $\log_b x$ answers “how many times must I multiply $b$ by itself to reach $x$?” That makes logs the natural tool for anything that grows by multiplying - and it is why a number that gets 10 times bigger moves only one step up a log scale. This tool finds the log in any base.

How It Works

$$\log_b(x) = \frac{\ln(x)}{\ln(b)} \quad \text{(change of base)}$$

For base 10 enter 10 (common log); for the natural log enter e ≈ 2.71828.

How to Use It

1. Enter the number.
2. Enter the base (10, 2, e, or any positive value other than 1).
3. Read the logarithm and the steps.

Worked Examples

Number	Base	Logarithm
1000	10	3
100	10	2
8	2	3
81	3	4

FAQ

How do you calculate a logarithm with any base?

Use the change-of-base formula $\log_b(x) = \frac{\ln(x)}{\ln(b)}$, which is how this tool works.

What is the difference between log and ln?

“log” usually means base 10 (the common log); “ln” is the natural log, base e ≈ 2.71828. Enter the base you need.

What is log base 2 of 8?

3, because $2^3 = 8$.