Logarytmy! Oblicz : [latex]2log_{3}sqrt{8} - 3log_{3}2= \ log_{8}2+4log_{8}sqrt{2}[/latex]   Proszę o jak najszybszą pomoc! Z gory dzięki wielkie :)  

2log(3)√8 -3log(3)2 = log(3)√8² - log(3)2³= =log(3)8 -.log(3)8 =log(3) 8/8 = log(3)1=0 bo:    3^x=1      3^x=3^0        x=0   log(8) 2 + 4log(8)√2 =log(8) 2 + log(8)√2⁴ = =log(8) 2 + log(8) 4 = log(8) (2*4) = log(8) 8 =1 bo   8^x=8        x=1

[latex]2log_{3}sqrt{8} - 3log_{3}2=2log_3(2^3)^frac12-log_32^3=\ =log_32^3-log_32^3=0\ log_{8}2+4log_{8}sqrt{2}=log_82+4log_82^frac12=log_82+log_82^2=\ =log_42+log_84=log_*(2cdot 4)=log_88=1\ \ Zastosowano nastepujace wlasnosci:\ n log_ab^m=log_ab^{mcdot n}\ log_ab+log_ac=log_a(bcdot c)\ log_aa=1\ sqrt{a}=a^{frac12}[/latex]