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c, \(5^{x+4}-3\cdot5^{x+3}=2\cdot5^{11}\)
\(\Leftrightarrow5^{x+3}\cdot5-3\cdot5^{x+3}=2\cdot5^{11}\)
\(\Leftrightarrow5^{x+3}\left(5-3\right)=2\cdot5^{11}\)
\(\Leftrightarrow5^{x+3}\cdot2=2\cdot5^{11}\)
\(\Leftrightarrow5^{x+3}=5^{11}\)
\(\Leftrightarrow x+3=11\)
\(\Leftrightarrow x=8\)
Vậy x = 8
d, \(2^x+2^{x+1}+2^{x+2}+2^{x+3}+2^{x+4}+2^{x+5}=480\)
\(\Leftrightarrow2^x\left(1+2+2^2+2^3+2^4+2^5\right)=480\)
\(\Leftrightarrow2^x\cdot63=480\)
\(\Leftrightarrow2^x=\frac{160}{21}\)
\(\Leftrightarrow x\approx2,93\)
a) 2/2.5 + 2/5.8 + 2/8.11 + ... + 2/x(x+3) = 7/23
3/2.5 + 3/5.8 + 3/8.11 + ... + 3/x(x+3) = 21/46
1/2 - 1/5 + 1/5 - 1/8 + 1/8 - 1/11 + ... + 1/x - 1/x+1 = 21/46
1/2 - 1/x+1 = 21/46
=> 1/x+1 = 1/23
=> x + 1 = 23
=> x = 22
Vậy x = 22.
b) 3/4 . x - 1/5 = 7/4 . x + 11/5
3/4 . x - 7/4 . x = 1/5 + 11/5
x (3/4 - 7/4) = 12/5
-x = 12/5
x = -12/5
Vậy x = -12/5.
c) {[(20 - 2.3).5] - 2.5} : 2 + (4.5)²
= {(20 - 6).5] - 10} : 2 + 20²
= (14.5 - 10) : 2 + 400
= (70 - 10) : 2 + 400
= 60 : 2 + 400
= 30 + 400
= 430
d) (1² + 2² + 3² + ... + 100²) . (2⁴ - 4²)
= (1² + 2² + 3² + ... + 100²) . (16 - 16)
= (1² + 2² + 3² + ... + 100²) . 0
= 0
Bài 2
a) -2x < 5
2x > 5
x > 5/2
b) [31 - (x + 5)].11 = 121
31 - (x + 5) = 121 : 11
31 - (x + 5) = 11
x + 5 = 31 - 11
x + 5 = 20
x = 20 - 5
x = 15
c) (x + 1)³ = 27
(x + 1)³ = 3³
x + 1 = 3
x = 3 - 1
x = 2
a: =>x-2/5=3/4:1/3=3/4*3=9/4
=>x=9/4+2/5=45/20+8/20=53/20
b: =>x-2/3=7/3:4/5=7/3*5/4=35/12
=>x=35/12+2/3=43/12
c: 1/3(x-2/5)=4/5
=>x-2/5=4/5*3=12/5
=>x=12/5+2/5=14/5
d: =>2/3x-1/3-1/4x+1/10=7/3
=>5/12x-7/30=7/3
=>5/12x=7/3+7/30=77/30
=>x=77/30:5/12=154/25
e: \(\Leftrightarrow x\cdot\dfrac{3}{7}-\dfrac{2}{7}+\dfrac{1}{2}-\dfrac{5}{4}x+\dfrac{5}{2}=0\)
=>\(x\cdot\dfrac{-23}{28}=\dfrac{2}{7}-3=\dfrac{-19}{7}\)
=>x=19/7:23/28=76/23
f: =>1/2x-3/2+1/3x-4/3+1/4x-5/4=1/5
=>13/12x=1/5+3/2+4/3+5/4=257/60
=>x=257/65
i: =>x^2-2/5x-x^2-2x+11/4=4/3
=>-12/5x=4/3-11/4=-17/12
=>x=17/12:12/5=85/144
c. Có \(\overline{ab}+\overline{ba}=10a+b+10b+a\)
\(=\left(10a+a\right)+\left(10b+b\right)\)
\(=11a+11b\)
\(=11.\left(a+b\right)\)
Ta thấy \(11.\left(a+b\right)⋮11\)
Vậy \(\overline{ab}+\overline{ba}⋮11\left(dpcm\right)\)
a: \(5C=5+5^2+5^3+...+5^{2018}\)
\(\Leftrightarrow4C=5^{2018}-1\)
\(\Leftrightarrow C=\dfrac{5^{2018}-1}{4}\)
\(\Leftrightarrow5^x-1=\dfrac{5^{2018}-1}{4}\)
\(\Leftrightarrow5^x=\dfrac{5^{2018}+3}{4}\)(vô lý)
c: \(64^{10}-32^{11}-16^{13}\)
\(=2^{60}-2^{55}-2^{52}\)
\(=2^{52}\left(2^8-2^3-1\right)\)
\(=2^{52}\cdot247⋮̸49\)
Bài 1
123.32
=(2.6)3.32
=23.63.32
=23.23.35
=23+3.35
=26.35
Bài 2:Tìm X
(x-2)5=243
(x-2)5=35
=>(x-2)=3
x =3+2
x =5
2x+2x+4=272
2x+2x+4=24+28
=> x =4
=12.12.12.3.3=3.4.3.4.3.4.3.3=3.3.3.3.3.4.4.4=3 mũ 5 . 4 mũ 3
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