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a) \(5x-65=5.3^2 \\ 5x-65=45\\5x=45+65\\5x=110\\x=22\)
b) \(200-(2x+6)=4^3\\2x+6=200-4^3\\2x+6=136\\2x=130\\x=65\)
c) \(2(x-51)=2.2^3+20\\2(x-51)=16+20\\2(x-51)=36\\x-51=18\\x=51+18=69\)
d) \(135-5(x+4)=35\\5(x+4)=135-45\\5(x-4)=90\\x-4=18\\x=18+4=22\)
e) \((2x-4)(15-3x)=0\\2(x-2).3(5-x)=0\\(x-2)(5-x)=0\\ \left[ \begin{array}{l}x-2=0\\5-x=0\end{array} \right. \\ \left[ \begin{array}{l}x=2\\x=5\end{array} \right.\)
f) \(2^{x+1} . 2^{2014}=2^{2016} \\ (2^{x+1} . 2^{2014}):2^{2014}=2^{2016} :2^{2014} \\ 2^{x=1}=2^{2016-2014} \\2^{x+1}=2^2\\x+1=2\\x=1\)
g) \(15+(x-1)^3=43\\(x-1)^3=15-42\\(x-1)^3=-27\\(x-1)^3=(-3)^3\\x-1=-3\\x=-2\)
h) \(15-x=17+(-9)\\15-x=17-9\\15-x=8\\x=15-8\\x=7\)
i) \(|x-5|=|-7|+|-4|\\|x-5|=7+4\\|x-5|=11\\ \left[ \begin{array}{l}x-5=11\\x-5=-11\end{array} \right. \\ \left[ \begin{array}{l}x=16\\x=-6\end{array} \right.\)
k) \(|x-3|-12=-9+|-7|\\|x-3|-12=-9+7\\|x-3|-12=-2\\|x-3|=10 \\ \left[ \begin{array}{l}x-3=10\\x-3=-10\end{array} \right. \\ \left[ \begin{array}{l}x=13\\x=-7\end{array} \right.\)
\(2x-49=5.32\\ \Leftrightarrow2x-49=160\\ \Leftrightarrow2x=209\\ \Leftrightarrow x=\dfrac{209}{2}\)
\(200-\left(2x+6\right)=43\\ \Leftrightarrow2x+6=157\\ \Leftrightarrow2x=151\\ \Leftrightarrow x=\dfrac{151}{2}\)
\(135-5\left(x+4\right)=35\\ \Leftrightarrow5\left(x+4\right)=100\\ \Leftrightarrow x+4=20\\ \Leftrightarrow x=16\)
Bài 2: Tìm số tự nhiên x biết:
a) 12(x−1)∶3=43+23 c) (7x−11)3=23.52+200
b) 128−3(x+4)=23 d) 2x+2−2x=96
a, x - 1 2 = 36
ó x - 1 2 = 6 2
ó x – 1 = 6
ó x = 7
Vậy x = 7
b, 7 x - 11 3 = 2 5 . 5 2 + 200
=> 7 x - 11 3 = 800 + 200
=> 7 x - 11 3 = 1000
=> 7 x - 11 3 = 10 3
=> 7x – 11 = 10
=> 7x = 21
=> x = 3
Vậy x = 3
c, x 11 = x
=> x 11 - x = 0
=> x ( x 10 - 1 ) = 0
=>
d, x 2 = 2 3 + 3 2 + 4 3
=> x 2 = 81
=> x = 9
e, 2 x 3 3 2 = 48
=> 2 x 3 9 = 48
=> 2 x 3 = 48 . 9
=> x 3 = 216
=> x 3 = 6 3
=> x = 6
f, 2 x + 1 3 = 125
=> 2 x + 1 3 = 5 3
=> 2x + 1 = 5
=> 2x = 4
=> x = 2
a) \(2^x:4=16\\ \Rightarrow2^x=64\\ \Rightarrow2^x=2^6\\ \Rightarrow x=6\)
b) \(4^{x-3}=256\\ \Rightarrow4^{x-3}=4^4\\ \Rightarrow x-3=4\\ \Rightarrow x=7\)
c) \(\left(2x+1\right)^3=343\\ \Rightarrow\left(2x+1\right)^3=7^3\\ \Rightarrow2x+1=7\\ \Rightarrow x=3\)
d) \(10+2x=4^5:4^3\\ \Rightarrow10+2x=16\\ \Rightarrow x=3\)
a,2^x:4=16
2^x=16.4=64
2^x=2^6
=>x=6
b,4^x-3=256
4^x-3=4^4
=>x-3=4
x=4+3=7
c,(2x+1)^3=343
(2x+1)^3=7^3
=>2x+1=7
2x=7-1=6
x=6:2=3
d,10+2x=4^5:4^3
10+2x=4^2=16
2x=16-10=6
x=6:2=3
a, 2x : 4 = 16
⇒ 2x : 22 = 24
⇒ x - 2 = 4
⇒ x = 6
b, 4x-3 = 256
⇒ 4x - 3 = 44
⇒ x - 3 = 4
⇒ x = 7
c, (2x + 1)3 = 343
⇒ (2x + 1)3 = 73
⇒ 2x + 1 = 7
⇒ 2x = 6
⇒ x = 3
d, 10 + 2x = 45 : 43
⇒ 10 + 2x = 16
⇒ 2x = 6
⇒ x = 3
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