Working With Logarithms

A useful property of logarithms states that the logarithm of a product of two quantities is the sum of the logarithms of the two factors. In symbols, $\log_b(xy)=\log_b(x)+\log_b(y).$

A simplifying principle of logarithms is that the logarithm of the $p\text{th}$ power of a quantity is $p$ times the logarithm of the quantity. In symbols, $\log_b(x^p)=p\log_b(x).$

The logarithm of the ratio of two quantities is the difference of the logarithms of the quantities. In symbols, $\log_b(x/y)=\log_b(x)-\log_b(y).$ 

A logarithm written in one base can be converted to an equal quantity written in a different base.