[tex]a) log_{ \frac{1}{3} }(0.5 \times 0.4 \times \frac{83 - 8}{0} ) = log_{ \frac{1}{3} }( \frac{1}{2} \times \frac{4}{5} \times \frac{75}{90} ) = log_{ \frac{1}{3} }(2 \times \frac{15}{90} ) = log_{ \frac{1}{3} }(2 \times \frac{1}{6} ) = log_{ \frac{1}{3} }( \frac{1}{3} ) = 1[/tex]
[tex]b) log_{ {2}^{ \frac{1}{2} } }( {2}^{ \frac{16}{3} } ) = \frac{32}{3} [/tex]
[tex]c) log_{0.5}( \frac{ \frac{5}{12} }{ \frac{80}{3} } ) = log_{ {2}^{ - 1} }( \frac{1}{64} ) = log_{ {2}^{ - 1} }( {2}^{ - 6} ) = 6[/tex]
[tex] d)\frac{ log_{5}(9) }{ log_{5}(3) } = \frac{ log_{5}( {3}^{2} ) }{ log_{5}(3) } = \frac{2 log_{5}(3) }{ log_{5}(3) } = 2[/tex]
