# How do you sum a logarithm?

**logarithms**states that the

**logarithm**of a product of two quantities is the

**sum**of the

**logarithms**of the two factors. In symbols,

**log**b(xy)=

**log**b(x)+

**log**b(y). ? ( x y ) =

**log**b ? ( x ) +

**log**b ?

Considering this, what happens when you add logarithms?

The laws apply to **logarithms** of any base but the same base must be used throughout a calculation. This law tells us how to **add** two **logarithms** together. **Adding** log A and log B results in the **logarithm** of the product of A and B, that is log AB. The same base, in this case 10, is used throughout the calculation.

**logarithm**of a number is the exponent that we need to raise the base in order to get the number.

**Logarithm**rules.

Rule name | Rule |
---|---|

Logarithm power rule | log_{b}(x ^{y}) = y ∙ log_{b}(x) |

Logarithm base switch rule | log_{b}(c) = 1 / log_{c}(b) |

Logarithm base change rule | log_{b}(x) = log_{c}(x) / log_{c}(b) |

Then, what is the property of log?

Recall that we use the product rule of exponents to combine the product of exponents by adding: xaxb=xa+b x a x b = x a + b . We have a similar **property** for **logarithms**, called the product rule for **logarithms**, which says that the logarithm of a product is equal to a sum of **logarithms**.

A logarithm is the power to which a **number** must be raised in order to get some other **number** (see Section 3 of this Math Review for more about exponents). For example, the base ten logarithm of 100 is 2, because ten raised to the power of two is 100: **log** 100 = 2. because.