Cho C= $2^{2}$ +$2^{3}$ +$2^{4}$ + …..+ $2^{99}$ +$2^{100}$ $\text{Tìm x để $2^{2x-1}$ -2=C}$

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1. $\text{C=2²+2³+….+$2^{99}$ +$2^{100}$}$

   -1C=2+$2^{2}$+….+ $2^{98}$ + $2^{99}$

   $\text{C+-1C=C=$2^{101}$-2}$

   $\text{⇒$2^{2x-1}$ – 2 = $2^{101}$-2}$

   $\text{⇒$2^{2x-1}$=$2^{101}$}$

   $\text{⇒2x-1=101}$

   $\text{⇒2x=102}$

   $\text{⇒x=51}$

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2. 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:

   $\begin{array}{l}\quad 2^{\displaystyle{2x-1}} -2 = C\\
   \to 2^{\displaystyle{2x-1}} -2 = 2^{101} – 2\\
   \to 2^{\displaystyle{2x-1}}= 2^{101}\\
   \to 2x – 1 = 101\\
   \to 2x = 102\\
   \to x = 51
   \end{array}$

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