# Binary Logarithm

Binary stands for 2. Therefore, the log function with base 2 is known as binary logarithm.

If 2$^{x}$ = n, then $log_{2}$ (n) = x is the binary logarithm.

For example, the binary log of 1 is zero since 2$^{0}$ = 1. Similarly, the binary log of 4 is 2 since 2$^{2}$ = 4 and hence so on.

We can easily convert bases of logs by a simple rule, that is, we can change base from 2 to some other number and vice versa as follows.

$log_{2}$ (n) = $\frac{ln n}{ln 2}$ = $\frac{log_{10} (n)}{log_{10} (2)}$

This way we can convert base from binary to natural log and also to base 10. Similarly we can base 10 or natural log to binary based logarithmic function.