Chapter 6 - Exponential, Logarithmic, And Inverse Trigonometric Functions - 6.1 Exponential And Logarithmic Functions - Exercises Set 6.1 - Page 418: 5

$$\left( {\bf{a}} \right)4,\,\,\,\left( {\bf{b}} \right) - 5,\,\,\,\left( {\bf{c}} \right)1,\,\,\,\left( {\bf{d}} \right)\frac{1}{2}$$

$$\eqalign{ & \left( {\bf{a}} \right){\log _2}16 \cr & {\text{write 16 as }}{{\text{2}}^4} \cr & = {\log _2}{2^4} \cr & {\text{use the logarithmic property }}\log {a^n} = n\log a \cr & = 4{\log _2}2 \cr & {\text{simplify}} \cr & = 4\left( 1 \right) \cr & = 4 \cr & \cr & \left( {\bf{b}} \right){\log _2}\left( {\frac{1}{{32}}} \right) \cr & {\text{write 32 as }}{{\text{2}}^5} \cr & = {\log _2}\left( {\frac{1}{{{2^5}}}} \right) \cr & {\text{use the exponential property }}\frac{1}{{{a^n}}} = {a^{ - n}} \cr & = {\log _2}{2^{ - 5}} \cr & {\text{use the logarithmic property }}\log {a^n} = n\log a \cr & = - 5{\log _2}2 \cr & {\text{simplify}} \cr & = - 5\left( 1 \right) \cr & = - 5 \cr & \cr & \left( {\bf{c}} \right){\log _4}4 \cr & {\text{use the logarithmic property }}{\log _a}a = 1 \cr & {\log _4}4 = 1 \cr & \cr & \left( {\bf{d}} \right){\log _9}3 \cr & {\text{write 3 as }}{{\text{9}}^{1/2}} \cr & = {\log _9}{9^{1/2}} \cr & {\text{use the logarithmic property }}\log {a^n} = n\log a \cr & = \frac{1}{2}{\log _9}9 \cr & {\text{simplify}} \cr & = \frac{1}{2}\left( 1 \right) \cr & = \frac{1}{2} \cr} $$