Example 16.5.

Express the following in logarithm notation: \(4^{3}=64\). \[4^{3}=64\iff \log _{4}64=3\]

Let \(M,N, a>0\) and \(n\) be any number

1.

\(\log _{\displaystyle {a}}MN =\log _{\displaystyle {a}}M+\log _{\displaystyle {a}}N\)

2.

\(\log _{\displaystyle {a}}\frac {M}{N}=\log _{\displaystyle {a}}M-\log _{\displaystyle {a}}N\)

3.

\(\log _{\displaystyle {a}}M^{\displaystyle {n}} = n\log _{\displaystyle {a}}M\)

4.

\(\log _{\displaystyle {a}}a=1\iff a^1=a\)

5.

\(\log _{\displaystyle {a}}1=0 \iff a^{0}=1\)