Question

Va rog!!
Ambele exerciții!!
Dau coroana!!!!:))

Answer 1

$\displaystyle 12)~\Big(4^9\Big)^{40}=2^{30x}\Rightarrow 4^{360}=2^{30x}\Rightarrow \Big(2^2\Big)^{360}=2^{30x}\Rightarrow 2^{720}=2^{30x}\Rightarrow \\\\ \Rightarrow 720=30x \Rightarrow x=\frac{720}{30}\Rightarrow x= 24 ~~~~~~~~~~~\boxed{b}$

$\displaystyle 13)~24+26+28+...+2022\\\\ a_n=a_1+(n-1) \cdot r\\\\ a_1=24,~r=26-24=2,~a_n=2022\\\\ 2022=24+(n-1) \cdot 2 \ \Rightarrow 2022=24+2n-2 \Rightarrow -2n=24-2-2022 \Rightarrow \\\\ \Rightarrow -2n=-2000 \Rightarrow n=\frac{2000}{2} \Rightarrow n=1000\\\\ S_n=\frac{(a_1+a_n)\cdot n}{2} \\\\24+26+28+...+2022=\frac{(24+2022)\cdot 1000}{2} =2046 \cdot 500=1023000~~~~\boxed{b}$