# Log rules

There are a number of logarithm rules, properties, and identities that can be used when working with logarithms. They can be particularly useful for manipulating and solving algebraic expressions or equations. Three basic logarithm rules are the product, quotient, and power rules.

## Product rule

The product rule of logarithms can be expressed as

log_{b}(mn) = log_{b}(m) + log_{b}(n)

where b is the base and m and n are variables being multiplied.

Example

Expand: log_{2}(7x).

log_{2}(7x) = log_{2}(7) + log_{2}(x)

## Quotient rule

The quotient rule of logarithms can be expressed as

log_{b}() = log_{b}(m) - log_{b}(n)

where b is the base and m is being divided by n.

Example

Expand: log_{16}().

log_{16}() = log_{16}(5) - log_{16}(y)

## Power rule

The power rule of logarithms can be expressed as

log_{b}(m^{n}) = n·log_{b}(m)

where b is the base and m is being raised to the n^{th} power.

Example

Expand: ln(12^{z}).

ln(12^{z}) = z·ln(12)

Note that "ln" is just "log_{e}."