# Logarithms

The logarithm of a number with a given base is the exponent to which it is necessary to raise the base in order to obtain the number.

**a** is the **base**, **x** is the **number** and **y** is the **logarithm**.

#### Calculate the Logarithm:

#### Common Logarithm

The **common logarithm** has a **base of 10**. It is represented by **log (x)**.

x | 0.001 | 0.01 | 0.1 | 1 | 10 | 100 | 100 |
---|---|---|---|---|---|---|---|

y = log x | −3 | −2 | −1 | 0 | 1 | 2 | 3 |

#### Natural Logarithm

The **natural logarithm** has a base of **e** (an irrational number with an approximate value of 2.718281828). It is represented by **ln (x). **

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