Question

Tìm x biết 2^x+2^x+1+...+2^x+2019=2^x+2023-8

Answer 1

Lời giải:

$2^x+2^{x+1}+2^{x+2}+...+2^{x+2019}=2^{x+2023}-8$

$2^x(1+2+2^2+...+2^{2019})=2^{x+2023}-8$

Xét:

$A=1+2+2^2+...+2^{2019}$

$2A=2+2^2+2^3+...+2^{2020}$

$\Rightarrow A=2A-A=2^{2020}-1$

Khi đó:

$2^x.A=2^{x+2023}-8$

$2^x(2^{2020}-1)=2^{x+2023}-2^3$

$2^x(2^{2023}-2^{2020}+1)-2^3=0$

$2^x(2^{2020}.7+1)=2^3$

$x$ ra số sẽ khá xấu. Bạn coi lại.