Laws of Logs

The properties of indices can be used to show that 

the following rules for logarithms are satisfied:

·         log_ax + log_ay = log_a(xy)

·         log_ax – log_ay = log_a(x/y)

·         log_axⁿ = n.log_ax

Example

Simplify: log 3 + 3log 2 - log 4

                 = log 3 + log 2³ - log 4

                 = log 2 + log 8 - log 4

                = log (2 × 8) - log 4

                = log 16 - log 4

                = log (16/4)
            
                = log 4