The following list of important logarithm laws should be memorized. Let $a>0$ and $a \neq 1$. Suppose that $p > 0$, $q > 0$ and $k$ are real numbers. We have the following logarithmic laws:
The logarithmic product law: $\log_{a}(pq) = \log_{a}(p)+\log_{a}(q)$
The logarithmic quotient law: $\displaystyle \log_{a}\left(\frac{p}{q}\right) = \log_{a}(p) - \log_{a}(q)$
The logarithmic power law: $\log_{a}(p^{k}) = k \log_{a}(p)$.
If you are taking calculus, these laws will be discussed in greater detail in this class.
Multiplication law of logs.
Division law of logs.
Power law of logs.
Combining log laws.