Oblicz wartość wyrażenia [latex] a) log_2_ }48 - log_2_}3 \ b) log_3 }frac{1}{6} + log_3} frac{2}{3} \ c) 2log_ frac{1}{2} } sqrt{3} + log_ frac{1}{2} } 5 frac{1}{3} \ d) (log_5}6-log_5}80)^{2} [/latex]

a) [latex]log_2_ }48 - log_2_}3=log_2(48:3)=log_216=[/latex] [latex]log_22^4=4log_22=4[/latex] b) [latex]log_3 }frac{1}{6} + log_3} frac{2}{3}=log_3left(frac{1}{6} cdotfrac{2}{3} ight)=log_3frac{1}{9}=[/latex] [latex]log_3left( frac{1}{3} ight)^2 =log_33^{-2}=-2log_33=-2[/latex] c) [latex]2log_ frac{1}{2} } sqrt{3} + log_ frac{1}{2} } 5 frac{1}{3}=log_ frac{1}{2} }( sqrt{3})^2 + log_ frac{1}{2} } frac{16}{3}=[/latex] [latex]log_ frac{1}{2} }3 + log_ frac{1}{2} } frac{16}{3}=log_ frac{1}{2} }left( 3 cdot frac{16}{3} ight) =[/latex] [latex]log_ frac{1}{2} }16=log_ frac{1}{2} }2^4=log_ frac{1}{2} }left( frac{1}{2} ight) ^{-4}=[/latex] [latex]-4log_ frac{1}{2} }frac{1}{2}=-4[/latex] d) [latex](log_5}16-log_5}80)^{2}=(log_5}(16:80))^{2}=[/latex] [latex](log_5} frac{1}{5} )^{2}=(log_5}5^{-1}} )^{2}=(-log_5}5 )^{2}=(-1)^2=1[/latex]