Zad 1: Oblicz a) [latex]log _{4} 2 [/latex] b) [latex]log _{4} 8[/latex] c) [latex]log _{4} frac{1}{1024} [/latex] d) [latex]log _{4} frac{1}{ sqrt{2} } [/latex] Proszę o pomoc, daję naj :)

a) [latex]log_42=log_44^{frac12}=frac12cdotlog_44=frac12cdot1=frac12[/latex] b) [latex]log_48=log_4(4cdot2)=log_44+log_42=1+frac12=frac32[/latex] c) [latex]log_4(frac1{1024})=log_4(frac1{4^5})=log_4(4^{-5})=-5cdotlog_44=-5cdot1=-5[/latex] d) [latex]log_4(frac1{sqrt2})=log_4[(sqrt2)^{-1})]=log_4[(2^{frac12})^{-1}]=log_4(2^{-frac12})=\=log_4[(4^{frac12})^{-frac12}]=log_44^{-frac14}=-frac14cdot1=-frac14[/latex]