Chapter 6 - Exponential, Logarithmic, And Inverse Trigonometric Functions - 6.1 Exponential And Logarithmic Functions - Exercises Set 6.1 - Page 419: 13

$$\log \left( {\frac{{256}}{3}} \right)$$

$$\eqalign{ & 4\log 2 - \log 3 + \log 16 \cr & {\text{use the power property for logarithms }}\log {a^n} = n\log a \cr & = \log {2^4} - \log 3 + \log 16 \cr & {\text{simplify}} \cr & = \log 16 - \log 3 + \log 16 \cr & {\text{use the quotient property for logarithms}} \cr & = \log \left( {\frac{{16}}{3}} \right) + \log 16 \cr & = \log \left( {\frac{{16}}{3}} \right) + \log 16 \cr & {\text{use the product property for logarithms}} \cr & = \log \left( {\frac{{16 \times 16}}{3}} \right) \cr & = \log \left( {\frac{{256}}{3}} \right) \cr} $$