1. Tìm \(x\):
a) 4\(x+1\) + 4\(x\) = 320 x 20140
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1: =>\(5^{2x-3}=5^2\cdot3+5^2\cdot2=5^2\cdot5=5^3\)
=>2x-3=3
=>2x=6
=>x=3
2: \(41-2^{x+1}=9\)
=>\(2^{x+1}=32\)
=>x+1=5
=>x=4
3: =>\(4^{x+2}=65-1=64\)
=>x+2=3
=>x=1
\(5^{2x-3}-2.5^2=5^2.3\\ 5^{2x-3}=5^2.3+5^2.2\\ 5^{2x-3}=5^2.\left(3+2\right)\\ 5^{2x-3}=5^2.5\\ 5^{2x-3}=5^3\\ \Rightarrow2x-3=3\\ 2x=3+3\\ 2x=6\\ x=\dfrac{6}{2}\\ Vậy:x=3\)
Bài 1:
a) \(\dfrac{9}{20}-\dfrac{8}{15}\times\dfrac{5}{12}\)
\(=\dfrac{9}{20}-\dfrac{2}{9}\)
\(=\dfrac{41}{180}\)
b) \(\dfrac{2}{3}\div\dfrac{4}{5}\div\dfrac{7}{12}\)
\(=\dfrac{2}{3}\times\dfrac{5}{4}\times\dfrac{12}{7}\)
\(=\dfrac{5}{6}\times\dfrac{12}{7}\)
\(=\dfrac{10}{7}\)
c) \(\dfrac{7}{9}\times\dfrac{1}{3}+\dfrac{7}{9}\times\dfrac{2}{3}\)
\(=\dfrac{7}{9}\times\left(\dfrac{1}{3}+\dfrac{2}{3}\right)\)
\(=\dfrac{7}{9}\times1\)
\(=\dfrac{7}{9}\)
Bài 2:
a) \(2\times\left(x-1\right)=4026\)
\(\left(x-1\right)=4026\div2\)
\(x-1=2013\)
\(x=2014\)
Vậy: \(x=2014\)
b) \(x\times3,7+6,3\times x=320\)
\(x\times\left(3,7+6,3\right)=320\)
\(x\times10=320\)
\(x=320\div10\)
\(x=32\)
Vậy: \(x=32\)
c) \(0,25\times3< 3< 1,02\)
\(\Leftrightarrow0,75< 3< 1,02\) ( S )
=> \(0,75< 1,02< 3\)
\(4^x+4^{x+1}=320\\ \Leftrightarrow4^x.\left(1+4\right)=320\\ \Leftrightarrow4^x.5=320\\ \Leftrightarrow4^x=\dfrac{320}{5}=64=4^3\\ Vậy:x=3\\ ----\\ 3^{x+3}-3^x=234\\ \Leftrightarrow3^x\left(3^3-1\right)=234\\ \Leftrightarrow3^x.26=234\\ \Leftrightarrow3^x=\dfrac{234}{26}=9=3^2\\ vậy:x=2\)
a) 52x - 3 - 2 . 52 = 52 . 3
x - 3/52 - 2 = 3
x = 3 + 2 + 3/52
x = 263/52
b) 740 / (x + 10) = 102 - 2 . 13
740 / (x + 10) = 76
x + 10 = 740 / 76
x + 10 = 185/19
x = 185/19 - 10
x = -5/19
c) 65 - 4x + 2 = 20140
65 - 4x = 20140 - 2
65 - 4x = 20138
4x = 65 - 20138
4x = -20073
x = -20073/4
d) 120 + 2 . (3x - 17) = 214
60 + 3 . x - 17 = 107
20 + x - 17/3 = 107/3
20 + x = 107/3 + 17/3
20 + x = 124/3
x = 124/3 - 20
x = 64/3
e) 41 - 2x + 1 = 9
42 - 2x = 9
21 - x = 9/2
x = 21 - 9/2
x = 33/2
=> 320 : (x - 1) = 100 : 4 + 15
=> 320 : (x - 1) = 25 + 15
=> 320 : (x - 1) = 40
=> x - 1 = 320 : 40
=> x - 1 = 8
=> x = 8 + 1
=> x = 9
Cái này dễ
320:(x-1)=(125-25):4+15
320:(x-1)=100:4+15
320:(x-1)=25+15
320:(x-1)=40
x-1=320:40
x-1=8
x=8+1
=>x=9
3 . 22x + 3 - 4x + 1 = 320
\(\Rightarrow\)3 . 2x + 1 . 2x + 1 . 2 - 4x + 1 = 320
\(\Rightarrow\)6 . 4x + 1 - 4x + 1 = 320
\(\Rightarrow\)5 . 4x + 1 = 320
\(\Rightarrow\)4x + 1 = 64
\(\Rightarrow\)4x + 1 = 43
\(\Rightarrow\)x + 1 = 3
\(\Leftrightarrow\)x = 2
x+100-4*24=320
x+100-96=320
x+100=320+96
x+100=416
x=416-100
x=316
(x+100) -4 + 4 + 22x4 = 320
(x+100)+88=320
x=320-188
x=132
4x+1 + 4x = 320 x 1
4 x 4x + 4x = 320
4x x 5 = 320
4x = 320 : 5
4x = 64
4x = 43
=> x = 3
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