Oblicz na podstawie definicji: a)[latex]log _{3} frac{1}{ sqrt{3} } [/latex] b)[latex]log _{4} frac{1}{1024} [/latex] c)[latex]log _{0,25} 16[/latex] d)[latex]log100000[/latex]

[latex]log _{3} frac{1}{ sqrt{3} }=log _{3} 3^{- frac{1}{3} } =- frac{1}{3} log_33=- frac{1}{3}[/latex] [latex]log _{4} frac{1}{1024} =log_{4} 4^{-5} =-5log_{4}4=-5[/latex] [latex]log _{0,25} 16=log _{0,25} 0,25^{-2} =-2log _{0,25}0,25=-2[/latex] [latex]log100000=log 10^{5} =5log10=5[/latex]