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đặt A=2^x +2^x+1 +.....+2^x+2021=2^x+2026-16
đặt 2A = 2^x+1 +2^x+2 +......+2^x+2022=2^x+2027-32
lấy 2A-A =2^x+2022-2^x=2^2026-16
vậy,ta suy ra x=4
![](https://rs.olm.vn/images/avt/0.png?1311)
=>\(2^x\left(1+2+2^2+...+2^{2021}\right)=2^4\left(2^{2022}-1\right)\)
=>2^x=2^4
=>x=4
![](https://rs.olm.vn/images/avt/0.png?1311)
Đặt \(A=2^x+2^{x+1}+...+2^{x+2021}=2^{x+2026-16}\)
Đặt \(2A=2^{x+1}+2^{x+2}+...+2^{x+2022}=2^{x+2027+32}\)
Ta lấy \(2A-A=2^{x+2022}-2^x=2^{2026-16}\)
\(\Rightarrow x=4\)
Vậy \(x=4\)
\(2VT=2^{x+1}+2^{x+2}+2^{x+3}+...+2^{x+2022}\)
\(VT=2VT-VT=2^{x+2022}-2^x\)
\(\Rightarrow2^{x+2022}-2^x=2^{2026}-16\)
\(\Leftrightarrow2^{2022}.2^x-2^x=2^{2026}-2^4\)
\(\Leftrightarrow2^x\left(2^{2022}-1\right)=2^4\left(2^{2022}-1\right)\)
\(\Leftrightarrow2^x=2^4\Rightarrow x=4\)
![](https://rs.olm.vn/images/avt/0.png?1311)
1. \(2^x-26=6\)
\(\Rightarrow2^x=6+26\)
\(\Rightarrow2^x=32\)
\(\Rightarrow2^x=2^5\)
\(\Rightarrow x=5\)
2. \(64\cdot4^x=16^8\)
\(\Rightarrow4^3\cdot4^x=4^{16}\)
\(\Rightarrow4^x=4^{16}:4^3\)
\(\Rightarrow4^x=4^{13}\)
\(\Rightarrow x=13\)
3. \(\left(2x-1\right)^4=16\)
\(\Rightarrow\left(2x-1\right)^4=2^4\)
\(\Rightarrow2x-1=2\)
\(\Rightarrow2x=3\)
\(\Rightarrow x=\dfrac{3}{2}\)
4. \(\left(2x+1\right)^3=125\)
\(\Rightarrow\left(2x+1\right)^3=5^3\)
\(\Rightarrow2x+1=5\)
\(\Rightarrow2x=4\)
\(\Rightarrow x=2\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\left(2x+1\right)^3=125\\ \Rightarrow\left(2x+1\right)^3=5^3\\ \Rightarrow2x+1=5\\ \Rightarrow2x=4\\ \Rightarrow x=2.\\ b,\left(2x-1\right)^4=16\\ \Rightarrow\left(2x-1\right)^4=2^4\\ \Rightarrow2x-1=2\\ \Rightarrow2x=3\\ \Rightarrow x=\dfrac{3}{2}.\\ c,6.3^x-2.3^x=36\\ \Rightarrow3^x.\left(6-2\right)=36\\ \Rightarrow3^x.4=36\\ \Rightarrow3^x=9\\ \Rightarrow3^x=3^2\\ \Rightarrow x=2.\\ d,2^{x+1}-2^x=32\\ \Rightarrow2^x.\left(2-1\right)=32\\ \Rightarrow2^x=2^5\\ \Rightarrow x=5.\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(a,\Rightarrow x=3\)
\(b,\Rightarrow2x-1=2\)
\(\Rightarrow2x=3\)
\(\Rightarrow x=\dfrac{3}{2}\)
\(c,\Rightarrow x-2=4\)
\(\Rightarrow x=6\)
\(d,\Rightarrow2x-3=3\)
\(\Rightarrow2x=6\)
\(\Rightarrow x=3\)
![](https://rs.olm.vn/images/avt/0.png?1311)
a)
22 - 3(1-2x) = 2
22 - 3 + 6x = 2
6x = 2 - 22 + 3
6x = -17
=> x = -17/6
Vậy...
b)
8 - 2x = -16 - 5x
8 + 16 = -5x + 2x
-3x = 24
=> x = -8
Vậy...
Chúc em học tốt!!!
\(22-3\left(1-2x\right)=2\)
\(\Leftrightarrow3\left(1-2x\right)=22-2\)
\(\Leftrightarrow3-6x=20\)
\(\Leftrightarrow6x=3-20\)
\(\Leftrightarrow6x=-17\)
\(\Leftrightarrow x=\frac{-17}{6}\)
\(\text{Vậy }x=\frac{-17}{6}\)
\(8-2x=-16-5x\)
\(\Leftrightarrow16+8=-5x+2x\)
\(\Leftrightarrow24=3x\)
\(\Leftrightarrow x=24\div3\)
\(\Leftrightarrow x=8\)
\(\text{Vậy }x=8\)
Trả lời:
\(\left(1-2x\right)^2=16\)
\(\Leftrightarrow\left(1-2x\right)^2=\left(\pm4\right)^2\)
\(\Leftrightarrow\orbr{\begin{cases}1-2x=4\\1-2x=-4\end{cases}\Leftrightarrow\orbr{\begin{cases}2x=-3\\2x=5\end{cases}\Leftrightarrow}\orbr{\begin{cases}x=-\frac{3}{2}\\x=\frac{5}{2}\end{cases}}}\)
Vậy x = - 3/2; x = 5/2
\(\left(1-2x\right)^2=16=\left(\pm4\right)^2\)
+, Trường hớp 1 : 1 - 2x = 4
---> x = -3/2
+, Tường hợp 2 : 1 - 2x = -4
---> x = 5/2
học tốt