There are following main logarithm formulas

  1. Logarithm product formula

\[log_a\left(xy\right)=log_a\left(x\right)+log_a\left(y\right)\]

2. Logarithm quotient formula

\[\log_a{\left(\frac{x}{y}\right)}\ =\log_a{\left(x\right)}\ -\ \log_a{\left(y\right)}\]

3. Logarithm power formula

\[\log_a{\left(x^y\right)}\ =\ y\ \bullet\log_a{x}\]

4. Logarithm base switch formula

\[\log_a{x}\ =\ \frac{1}{\log_x{a}}\]

5. Logarithm base change formula

\[\log_a{(x)}\ =\frac{\log_b{(x)}}{\log_b{(a)}}\]

6. Logarithm of 0 formula

\[ \log_a{(0)} = undefined\]

7. Logarithm of 1 formula

\[ \log_a{(1)} = 0\]