Câu hỏi của Trần Duy Quân

Question

Rút gọn rồi tính x biết : $A=2^x-2$$A=2+2^2+...+2^{60}$

Nguyễn Huy Tú · Accepted Answer

Ta có:$A=2+2^2+...+2^{60}$$\Rightarrow2A=2^2+2^3+...+2^{61}$$\Rightarrow2A-A=\left(2^2+2^3+...+2^{61}\right)-\left(2+2^2+...+2^{60}\right)$$\Rightarrow A=2^{61}-2$Mà $A=2^x-2$$\Rightarrow2^{61}=2^x$$\Rightarrow x=61$Vậy x = 61Câu trả lời: Ta có:$A=2+2^2+...+2^{60}$$\Rightarrow2A=2^2+2^3+...+2^{61}$$\Rightarrow2A-A=\left(2^2+2^3+...+2^{61}\right)-\left(2+2^2+...+2^{60}\right)$$\Rightarrow A=2^{61}-2$Mà $A=2^x-2$$\Rightarrow2^{61}=2^x$$\Rightarrow x=61$Vậy x = 61

Trần Quỳnh Mai · Answer

$A=2+2^2+2^3+...+2^{60}$$\Rightarrow2A=\left(2.2\right)+\left(2.2^2\right)+\left(2.2^3\right)+...+\left(2.2^{60}\right)$$\Rightarrow2A=2^2+2^3+2^4+...+2^{61}$$\Rightarrow2A-A=\left(2^2+2^3+2^4+...+2^{61}\right)-\left(2+2^2+2^3+...+2^{60}\right)$$\Rightarrow A=2^{61}-2$Ta có :$A=2^x-2$$\Rightarrow2^{61}-2=2^x-2$$\Rightarrow2^{61}=2^x$$\Rightarrow x=61$Vậy x = 61Câu trả lời: $A=2+2^2+2^3+...+2^{60}$$\Rightarrow2A=\left(2.2\right)+\left(2.2^2\right)+\left(2.2^3\right)+...+\left(2.2^{60}\right)$$\Rightarrow2A=2^2+2^3+2^4+...+2^{61}$$\Rightarrow2A-A=\left(2^2+2^3+2^4+...+2^{61}\right)-\left(2+2^2+2^3+...+2^{60}\right)$$\Rightarrow A=2^{61}-2$Ta có :$A=2^x-2$$\Rightarrow2^{61}-2=2^x-2$$\Rightarrow2^{61}=2^x$$\Rightarrow x=61$Vậy x = 61

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