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\(5.5^{2x+2}=125\)
\(=>5^{2x+2}=125:5\)
\(=>5^{2x+2}=25=5^2\)
\(=>2x+2=2\)
\(=>2x=2-2\)
\(=>2x=0\)
\(=>x=0:2\)
\(=>x=0\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(1+5^2+5^4+...+5^{2x}\left(1\right)=\dfrac{25^6-1}{24}\)
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: \(A=\dfrac{25^6-1}{24}\)
\(\Rightarrow\dfrac{5^{2x+2}-1}{24}=\dfrac{\left(5^2\right)^6-1}{24}\)
\(\Rightarrow5^{2x+2}-1=5^{12}-1\)
\(\Rightarrow5^{2x+2}=5^{12}\)
\(\Rightarrow2x+2=12\)
\(\Rightarrow2x=10\)
\(\Rightarrow x=\dfrac{10}{2}\)
\(\Rightarrow x=5\)
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a, \(x+45=54\Leftrightarrow x=9\)
b, \(x+9=3\Leftrightarrow x=-6\)
c, \(5^{2x}=5^2\Rightarrow2x=2\Leftrightarrow x=1\)
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a). 5x = 125
=>5x = 53
=> x = 3
b) 32x = 81
=> 32x = 34
=> 2x = 4
=> x = 2
c). 52x-3 – 2.52 = 52 .3
=>52x: 53 = 52 .3 + 2.52
=>52x: 53 = 52 .5
=>52x = 52 .5.53
=>52x = 56
=> 2x = 6
=> x=3
a) 5x = 125
x = 125 : 5
x = 25
b) 32x = 81
x = 81 : 32
x = 81/ 32
c) 52x - 3 - 2.52 = 52.3
52x - 3 - 104 = 156
x - 3 - 104 = 156 : 52
x - 3 - 104 = 3
x - 3 = 3 + 104
x - 3 = 107
x = 107 + 3
x = 110
Ko chắc lắm , sai thì Sorry nhé .
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Ta có: 100 < 52x – 1 < 56
=> 52 < 100 < 52x-1 < 56
=> 2 < 2x – 1 < 6
=> 2 + 1 < 2x < 6 + 1
=> 3 < 2x < 7
Vì x ∈ N nên suy ra: x ∈ {2; 3} là thỏa mãn.
Ta có 100=52.4
\(\Rightarrow5^3\le5^{2x-1}< 5^6\)
\(\Rightarrow3\le2x-1< 6\)
\(\Rightarrow4\le2x< 7\)
\(\Rightarrow2\le x< 3,5\)
Mà \(x\) là số tự nhiên
\(\Rightarrow x=2\) hoặc \(x=3\)
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Ây, phần c) mìnk lộn, làm lại nè:
c) 42 + 23 . ( 168 : 22 - 62) = 16 + 8 . ( 168 : 4 - 36 )
= 16 + 8 . ( 42 - 36)
= 16 + 8 . 6
= 16 + 48
= 64
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#\(N\)
`a, -677*54+54.(-125)+2.54`
`=54.(-677+-125+2)`
`=54.(-800)`
`=-43200`
`b, -(324-267+252)+(133-76)`
`=-324+267-252+133-76`
`= (-324+-76)+(133+267)-252`
`=-400+400-252`
`=-252`
a: =54(-677-125+2)
=54*(-800)
=-43200
b: =-324+267-252+133-76
=-400+400-252
=-252
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\(5^{2x+1}.5^{x+1}=5^{17}\)
\(\Rightarrow5^{2x+1+x+1}=5^{17}\)
\(\Rightarrow5^{3x+2}=5^{17}\)
\(\Rightarrow3x+2=17\)
\(\Rightarrow3x=15\Rightarrow x=5\)
![](https://rs.olm.vn/images/avt/0.png?1311)
a) Ta có : ( -54 ) . ( 1-234 ) - 234 . 54
= ( -54 ) . ( -233 ) - 234 . 54
= 54 . 233 - 234 . 54
= 54. ( 233 - 234 )
= 54 . ( -1 )
= -54
b) Ta có : ( - 4 ) . ( + 125 ) . ( -25 ) . ( - 6 ) . ( -8)
= [ ( -4 ) .( -25 )] . [ ( 125 . ( - 8) ] . ( -6 )
= 100 . ( -1000 ) . ( - 6 )
= ( - 100000 ) . ( -6 )
= 600000
\(5^{2x-1}=125\cdot5^4\)
\(\Leftrightarrow2x-1=7\)
hay x=4