# Definition:General Logarithm/Binary

(Redirected from Definition:Binary Logarithm)

## Definition

Logarithms base $2$ are becoming increasingly important in computer science.

They are often referred to as binary logarithms.

## Also denoted as

A notation which is starting to take hold for the binary logarithm of $x$ is $\lg x$.

Some authors, particularly in the field of communication theory and cryptography, have been known to use the notation $\map \log x$ to denote $\log_2 x$, but this is not endorsed on $\mathsf{Pr} \infty \mathsf{fWiki}$.

## Examples

### Binary Logarithm: $\log_2 10$

The binary logarithm of $10$ is:

$\log_2 10 \approx 3 \cdotp 32192 \, 80948 \, 87362 \, 34787 \, 0319 \ldots$

### Binary Logarithm: $\log_2 32$

The binary logarithm of $32$ is:

$\lg 32 = 5$

## Also see

• Results about logarithms can be found here.

## Historical Note

The use of $\lg x$ instead of $\log_2 x$ to denote the binary logarithm was suggested by Edward M. Reingold, and adopted by Donald E. Knuth in his The Art of Computer Programming.