Question

[Thanhkhiem Tran]

Tìm X biết :2^x_1=A

Biết A =2⁰+2¹+2²+......+2¹¹¹+2¹¹²

Answer 1

[Không Tên]

\(A=2^0+2^1+2^2+...+2^{111}+2^{112}\)

=>  \(2A=2^1+2^2+2^3+...+2^{112}+2^{113}\)

=>  \(2A-A=\left(2^1+2^2+...+2^{113}\right)-\left(2^0+2^1+....+2^{112}\right)\)

=>  \(A=2^{113}-1\)

Vậy  \(x=113\)

Answer 2

[khai]

\(A=2^0+2^1+2^2+...+2^{111}+2^{112}\left(1\right)\)

\(\Rightarrow2A=2^1+2^2+2^3+...+2^{112}+2^{113}\left(2\right)\)

Trừ vế với vế (2) cho (1) ta được

\(2A-A=2^{113}-2^0\)

\(\Leftrightarrow A=2^{113}-1\)

\(\Rightarrow2^x-1=2^{113}-1\)

\(\Leftrightarrow x=113\)

Vậy \(x=113\)