Đáp án:
$x = 51$
Giải thích các bước giải:
Sửa đề:
$C=2+ 2^2 + 2^3 + 2^4 + \dots +2^{99} + 2^{100}$
Ta có:
$\begin{array}{l}\quad C= 2 + 2^2 + 2^3 + \dots +2^{99} + 2^{100}\\
\to 2C = 2^2+2^3 + 2^4+\dots + 2^{100}+ 2^{101}\\
\to 2C - C = (2^2 +2^3 + 2^4 + 2^5 +\dots + 2^{100}+ 2^{101}) - (2+ 2^2 + 2^3 + 2^4 + \dots +2^{99} + 2^{100})\\
\to C = 2^{101} - 2\end{array}$
Ta được:
$\begin{array}{l}\quad 2^{\displaystyle{2x-1}} -2 = C\\
\to 2^{\displaystyle{2x-1}} -2 = 2^{101} - 2\\
\to 2^{\displaystyle{2x-1}}= 2^{101}\\
\to 2x - 1 = 101\\
\to 2x = 102\\
\to x = 51
\end{array}$
