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Table of Contents

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## Definitions

### General

The binary logarithm of a number x, is a power p so that 2^{p}= x. In modern notation binary logarithm is written as . Any positive real number has a binary logarithm. The binary logarithm of 1 is 0, while the binary logarithm of 0 approaches negative infinity.

The graph of the binary logarithm function is shown in the figure below. It is a monotonic function.

### Properties

The derivative of the binary logarithm function is:

The integral of the binary logarithm function is given by: