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a) 5 + 45(2x - 1) = 10
45(2x - 1) = 10 - 5
45(2x - 1) = 5
2x - 1 = 5 : 45
2x - 1 = 1/9
2x = 1/9 + 1
2x = 10/9
x = 10/9 : 2
x = 5/9
b) 54 : (2ˣ⁻³ + 1) + 3 = 9
54 : (2ˣ⁻³ + 1) = 9 - 3
54 : (2ˣ⁻³ + 1) = 6
2ˣ⁻³ + 1 = 54 : 6
2ˣ⁻³ + 1 = 9
2ˣ⁻³ = 9 - 1
2ˣ⁻³ = 8
2ˣ⁻³ = 2³
x - 3 = 3
x = 3 + 3
x = 6
c) 14 + 36 : 3ˣ⁻⁵ = 18
36 : 3ˣ⁻⁵ = 18 - 14
36 : 3ˣ⁻⁵ = 4
3ˣ⁻⁵ = 36 : 4
3ˣ⁻⁵ = 9
3ˣ⁻⁵ = 3²
x - 5 = 2
x = 2 + 5
x = 7
a: =>45(2x-1)=5
=>2x-1=1/9
=>2x=10/9
=>x=5/9
b: =>\(\dfrac{54}{2^{x-3}+1}=6\)
=>\(2^{x-3}+1=9\)
=>\(2^{x-3}=8\)
=>x-3=3
=>x=6
c: \(14+36:3^{x-5}=18\)
=>\(\dfrac{36}{3^{x-5}}=18-14=4\)
=>\(3^{x-5}=9\)
=>x-5=2
=>x=7
= ( -25) x 1 +72 x (-25) + (-25) x27
= (- 25) x ( 1 + 72 + 27 )
= (-25) x 100
=-2500
b
c 37 x ( 25 + 37 ) - 27 x ( 37 + 25 )
= 37 x 25 + 37 x 37 -27x37 -27x25
= ( 37 x25 -27x25 )+(37x37-27+37)
=25 x ( 37 -27 ) + 37 x (37 - 27)
= 25 x10 + 37x10
= 250 + 370
= 770
a) =-25.( 1+72+27)
=-25.100= - 2500
b) = -36.45 + (-36) . 15 - (-36) . 40
= - 36. ( 45+15-40)
= -36 . 20= -720
c) =37.62 - 27 .62
= 62. ( 37 - 27 )
= 62 . 10
= 620
\(1+5^2+5^4+...+5^{2x}\left(1\right)=\dfrac{25^6-1}{24}\)
Đặt \(\left(1\right)=A\)
\(\Rightarrow A=1+5^2+...+5^{2x}\)
\(\Rightarrow5^2A=5^2+5^4+...+5^{2x+2}\)
\(\Rightarrow25A=5^2+5^4+...+5^{2x+2}\)
\(\Rightarrow25A-A=5^2+5^4+...+5^{2x+2}-1-5^2-...-5^{2x}\)
\(\Rightarrow24A=5^{2x+2}-1\)
\(\Rightarrow A=\dfrac{5^{2x+2}-1}{24}\)
Mà: \(A=\dfrac{25^6-1}{24}\)
\(\Rightarrow\dfrac{5^{2x+2}-1}{24}=\dfrac{\left(5^2\right)^6-1}{24}\)
\(\Rightarrow5^{2x+2}-1=5^{12}-1\)
\(\Rightarrow5^{2x+2}=5^{12}\)
\(\Rightarrow2x+2=12\)
\(\Rightarrow2x=10\)
\(\Rightarrow x=\dfrac{10}{2}\)
\(\Rightarrow x=5\)
a, 568 + 568 x 135 - 568 x 36
= 568 x ( 1 + 135 - 36)
= 568 x 100
56 800
b, 17 x 49 + 49 x 37 + 54 x 26 + 54 x 25
= 49 x ( 17 + 37) + 54 x ( 26 + 25 )
= 49 x 54 + 54 x 51
= 54 x ( 49 + 51)
= 54 x 100
= 5 400
c, 14 x 35 x 5 + 10 x 25 x 7 + 20 x 70
= ( 2 x 35) x ( 7 x 5) + ( 10 x 7) x 25 + 20 x 70
= 70 x 35 + 70 x 25 + 20 x 70
= 70 x ( 35 + 25 + 20)
= 70 x 80
= 5 600
a) 568 + 568 x 135 - 568 x 36
= 568 x ( 1+1+135-1-36 )
=568 x 100
=5680
b) 17 x 49 + 49 x 37 + 54 x 26 + 54 x 25
= 49 x ( 17 + 37 ) + 54 x ( 26 + 25 )
= 49 x 54 + 54 x 51
= 54 x ( 49 + 51 )
= 54 x 100
= 5400
c) 14 x 35 x 5 + 10 x 25 x 7 + 20 x 70
= 70 x 35 + 10 x 25 x 7+ 20 x 70
= 70 x 35 + 250 x 7 + 20 x 70
= 70 x 35 + 70 x 25 + 20 x 70
= 70 x (35+25+20)
= 70 x 80
= 5600
a, \(x+45=54\Leftrightarrow x=9\)
b, \(x+9=3\Leftrightarrow x=-6\)
c, \(5^{2x}=5^2\Rightarrow2x=2\Leftrightarrow x=1\)
\(a,\left(x+45\right)-54=0\\ \Rightarrow x+45=54\\ \Rightarrow x=9\\ b,12\left(x+9\right)=36\\ \Rightarrow x+9=3\\ \Rightarrow x=-6\\ c,5^{2x}=25\\ \Rightarrow5^{2x}=5^2\\ \Rightarrow2x=2\\ \Rightarrow x=1\)