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
logb(mn) = logb(m) + logb(n)
where b is the base and m and n are variables being multiplied.
Example
Expand: log2(7x).
log2(7x) = log2(7) + log2(x)
Quotient rule
The quotient rule of logarithms can be expressed as
logb(
) = logb(m) - logb(n)
where b is the base and m is being divided by n.
Example
Expand: log16(
).
log16() = log16(5) - log16(y)
Power rule
The power rule of logarithms can be expressed as
logb(mn) = n·logb(m)
where b is the base and m is being raised to the nth power.
Example
Expand: ln(12z).
ln(12z) = z·ln(12)
Note that "ln" is just "loge."