# Log Calculator

URL: https://speedycalculator.com/calculators/math/logarithm/
Last updated: 2026-10-25

> The log calculator finds the logarithm of a number in any base, plus the natural log (ln), common log (log₁₀) and binary log (log₂). Type a result to find the number it came from (the antilog).

## Inputs

- Number
- Base

## Results

- log_b(x)
- Natural log ln(x)
- log₁₀(x)
- log₂(x)

## Formula

```
log_b(x) = ln(x) ÷ ln(b)
```

## Explanation

A logarithm answers “to what power must the base be raised to get this number?” It turns multiplication into addition.

### How to use the Log Calculator

- **Number**
- **Base**
- Want to work backwards? Type a value into **log_b(x)** and **Number** is calculated for you.

Results update as you type, and every field accepts the units shown in its menu.

### How it works

The change-of-base formula divides the natural log of x by the natural log of the base.

### Inputs explained

FieldWhat to enterNumberA numberBaseA number

### What each result means

- **log_b(x)** = [Natural log ln(x)]([Number]) ÷ [Natural log ln(x)]([Base])
- **Natural log ln(x)** = [Natural log ln(x)]([Number])
- **log₁₀(x)** = log10([Number])
- **log₂(x)** = [Natural log ln(x)]([Number])÷[Natural log ln(x)](2)

### Example values

How the main result changes when **Number** changes and everything else stays at the example values above:

Numberlog_b(x)5002.6997502.87511,00031,2503.09691,5003.17612,0003.301

## Worked example

Inputs — Number: 1,000; Base: 10.

Results — **log_b(x) = 3**; Natural log ln(x) = 6.90775528; log₁₀(x) = 3; log₂(x) = 9.96578428.

## Key terms

- **Natural log**: Logarithm with base e ≈ 2.71828.

## FAQ

**What is the log of a negative number?**
Not defined among real numbers.

**What is an antilog?**
The inverse: if log_b(x) = y, then x = b^y.

**What formula does the Log Calculator use?**
log_b(x) = ln(x) ÷ ln(b).

**Can I work backwards from the result?**
Yes. Type the result you want into log_b(x) and the calculator finds the matching number.