1. [latex]a_1=8\r=5[/latex] [latex]a_4=a_1+3r\a_4=8+3cdot5=23[/latex] [latex]a_{17}=a_1+16r\a_{17}=8+16cdot5=88[/latex] [latex]S_4=frac{8+23}{2}cdot4=62[/latex] [latex]S_{17}=frac{8+88}{2}cdot17=816[/latex] [latex]a_5+a_6+...+a_{17}=S_{17}-S_4=816-62=754[/latex] 2. a) [latex]log_22+log_26-log_23=log_2(2cdot6:3)=log_24=2[/latex] b) [latex](log_85+log_86):(log_860-log_82)=log_8frac{5cdot6}{60:2}=\=log_8frac{30}{30}=log_81=0[/latex] c) [latex]2log_24+log_22-log_24=log_2(4^2cdot2:4)=log_28=3[/latex]
1. [latex]a_{5}=a_{1}+4r=8+4cdot 5=28\ a_{17}=a_{1}+16r=8+16cdot 5=88\ \ n=17-5=13\ \ S=frac{a_{5}+a_{17}}{2}cdot n=frac{28+88}{2}cdot 13=56cdot 13=754[/latex] 2 [latex]A)\ log_{2}2+log_{2}6-log_{2}3=log_{2}frac{2cdot 6}{3}=log_{2}4=log_{2}2^2=2\ \ B)\ (log_{8}5+log_{8}6):(log_{8}60-log_{8}2)=log_{8}(5cdot 6) : log_{8}frac{60}{2}=\=log_{8}30:log_{8}30=log_{8}1=log_{8}8^0=0\ \ C)\ 2log_{2}4+log_{2}2-log_{2}4=log_{2}frac{4^2cdot2}{4}=log_{2}8=log_{2}2^3=3[/latex]
1.w ciągu arytmetycznym (an) wyraz a1=8 i różnica r=5. oblicz sumę wyrazów od 5 do 17 włącznie 2.oblicz: A) log₂2+log₂6-log₂3= B) (log₈5+log₈6) : (log₈60-log₈2)= C) 2log₂4+log₂2-log₂4=...
