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Ta có -2-(x-17)=34-(-x+25)
-2-x+17=34+x+25
-2 +(-x)+17+(-x)=34+25
[(-x)+(-x)]+[(-2)+17]=29
(-x).2+15=29
(-x).2=29-15
(-x).2=14
(-x)=14:2
(-x)=7
x=-7
a) Đặt: \(A=1+2^2+2^3+...+2^{10}\)
\(\Rightarrow2A=2\left(1+2^2+2^3+...+2^9+2^{10}\right)\)
\(\Rightarrow2A=2+2^3+2^4+...+2^{10}+2^{11}\)
\(\Rightarrow2A-A=\left(2+2^3+2^4+...+2^{10}+2^{11}\right)-\left(1+2^2+2^3+...+2^{10}\right)\)
\(\Rightarrow A=\left(2^3-2^3\right)+\left(2^4-2^4\right)+...+\left(2-1\right)+\left(2^{11}-2^2\right)\)
\(\Rightarrow A=0+0+...+1+\left(2^{11}-2^2\right)\)
\(\Rightarrow A=1+2^{11}-2^2=1+2048-4=2045\)
Vậy: \(1+2^2+2^3+...+2^{10}=2045\)
b)
a] \(60-3\left(x-1\right)=2^3\cdot3\)
\(\Rightarrow60-3\left(x-1\right)=24\)
\(\Rightarrow3\left(x-1\right)=36\)
\(\Rightarrow x-1=12\)
\(\Rightarrow x=13\)
b] \(\left(3x-2\right)^3=2\cdot2^5\)
\(\Rightarrow\left(3x-2\right)^3=2^6\)
\(\Rightarrow\left(3x-2\right)^3=\left(2^2\right)^3\)
\(\Rightarrow3x-2=2^2\)
\(\Rightarrow3x=6\)
\(x=2\)
c] \(5^{x+1}-5^x=500\)
\(\Rightarrow5^x\left(5-1\right)=500\)
\(\Rightarrow5^x\cdot4=500\)
\(\Rightarrow5^x=125\)
\(\Rightarrow5^x=5^3\)
\(\Rightarrow x=3\)
d] \(x^2=x^4\)
\(\Rightarrow x=x^2\)
\(\Rightarrow x-x^2=0\)
\(\Rightarrow x\left(1-x\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x=0\\1-x=0\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=0\\x=1\end{matrix}\right.\)
a) \(2^2.2^4.x=16^2\)
\(2^6x=\left(2^4\right)^2\)
\(2^6.x=2^8\)
\(x=2^8:2^6\)
\(x=2^2\)
\(x=4\)
vay \(x=4\)
b) \(5^{2x+1}=125\)
\(5^{2x+1}=5^3\)
\(\Rightarrow2x+1=3\)
\(\Rightarrow2x=2\)
\(\Rightarrow x=1\)
vay \(x=1\)
c) \(\left(2x-1\right)^3=64\)
\(\left(2x-1\right)^3=4^3\)
\(\Rightarrow2x-1=4\)
\(\Rightarrow2x=5\)
\(\Rightarrow x=\frac{5}{2}\)
vay \(x=\frac{5}{2}\)
1.Tính nhanh nếu có thể:
a) 22 + 23 + 89 + 77
= ( 77 + 23 ) + 22 + 89
= 100 + 22 + 89
= 122 + 89
= 211
b) 35 . 15 + 15 . 65
= 15 . ( 35 + 65 )
= 15 . 100
= 1500
c) 7^2 - 36 : 3^2
= 7^2 - 36 : 9
= 7^2 - 4
= 49 - 4
= 45
d) 476 - {5 . [409 - (8 . 3 - 21)2] - 1724}
= 476 - {5 . [409 - (24 - 21)^2] - 1724}
= 476 - {5 . [409 - (3^2)] - 1724}
= 476 - {5 . [409 - 9 ] - 1724}
= 476 - {5. 400 - 1724}
= 476 - {2000 - 1724}
= 476 - 276
= 200
a: \(2\left(x-51\right)=2\cdot2^3+20\)
=>\(2\left(x-51\right)=2^4+20=36\)
=>x-51=36/2=18
=>x=18+51=69
b: \(2x-49=5\cdot3^2\)
=>\(2x-49=5\cdot9=45\)
=>2x=45+49=94
=>x=94/2=47
c: \(\left[\left(8x-12\right):4\right]\cdot3^3=3^6\)
=>\(\left[4\cdot\dfrac{\left(2x-3\right)}{4}\right]=3^3\)
=>\(2x-3=3^3=27\)
=>2x=3+27=30
=>x=30/2=15
d: \(2^{x+1}-2^2=32\)
=>\(2^{x+1}=32+2^2=32+4=36\)
=>\(x+1=log_236\)
=>\(x=log_236-1\)
e: \(\left(x^3-77\right):4=5\)
=>\(x^3-77=20\)
=>\(x^3=77+20=97\)
=>\(x=\sqrt[3]{97}\)
a) 22.23.x=82
22.23.x= 26
25.x = 26
x = 26:25
x = 2
b) 5x-1.52= 252
5x-1.52 = 54
5x-1 = 54: 52
5x-1 = 52
=> x-1=2
x = 2+1
x = 3
c)(2x-1)3=125
(2x-1)3= 53
=> 2x-1=5
2x = 5+1
2x = 6
x = 6:2
x = 3
d) 8x.2x=44
(8.2)x= 44
16x = 44
16x = 256
16x = 162
=> x=2
e) (x2.53)2 = 56
x2.2. 53.2= 56
x4 . 56 = 56
x4 = 56:56
x4 = 50
x4 =1
=> x=1