3.(4-x)-2.(x-1)=x+20
4.(2x+7)-3(3x-2)=24
3.(x-2)+2x=10
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LM
Lê Minh Vũ
CTVHS
VIP
2 tháng 8 2023
a) \(\left(2x-3\right)^2=16\)
\(\left(2x-3\right)^2=4^2\)
\(2x-3=4\)
\(2x=7\)
\(x=\dfrac{7}{2}=3,5\)
b) \(\left(3x-2\right)^5=-243\)
\(\left(3x-2\right)^5=-3^5\)
\(3x-2=-3\)
\(3x=-1\)
\(3x=-\dfrac{1}{3}\)
c) \(\left(x-7\right)^{x+1}=\left(x-7\right)^{x+11}\)
\(\left(x-7\right)^{x+1}-\left(x-7\right)^{x+11}=0\)
\(\left(x-7\right)^{x+1}\times\left[1-\left(x-7\right)^{10}\right]=0\)
\(\left(x-7\right)^{x+1}=0\) ; \(1-\left(x-7\right)^{10}=0\)
\(x-7=0;\left(x-7\right)^{10}=1\)
\(x=7;\left(x-7=1;x-7=-1\right)\)
\(x=7;x=8;x=6\)
NT
Nguyễn Thị Thương Hoài
Giáo viên
VIP
2 tháng 8 2023
a, (2\(x\) - 3)2 = 16
\(\left[{}\begin{matrix}2x-3=-4\\2x-3=4\end{matrix}\right.\)
\(\left[{}\begin{matrix}2x=-1\\2x=7\end{matrix}\right.\)
\(\left[{}\begin{matrix}x=-\dfrac{1}{2}\\x=\dfrac{7}{2}\end{matrix}\right.\)
Vậy \(x\in\){ - \(\dfrac{1}{2}\); \(\dfrac{7}{2}\)}
b, (3\(x\) - 2)5 = -243
( 3\(x\) - 2)5 = (-3)5
3\(x\) - 2 = -3
3 \(x\) = -1
\(x\) = - \(\dfrac{1}{3}\)
Vậy \(x\) = -\(\dfrac{1}{3}\)
c, \(\left(x-7\right)\)\(x+1\) = (\(x-7\))\(x+11\)
(\(x-7\))\(^{x+1}\).( \(\left(x-7\right)^{10}\) - 1 ) = 0
\(\left[{}\begin{matrix}\left(x-7\right)^{x+1}=0\\\left(x-7\right)^{10}=1\end{matrix}\right.\)
\(\left[{}\begin{matrix}x=7\\x-7=-1\\x-7=1\end{matrix}\right.\)
\(\left[{}\begin{matrix}x=7\\x=6\\x=8\end{matrix}\right.\)
Vậy \(x\in\){ 6; 7; 8}
2 tháng 8 2023
1: =>3^x=81
=>x=4
2: =>2^x=8
=>x=3
3: =>x^3=2^3
=>x=2
4: =>x^20-x=0
=>x(x^19-1)=0
=>x=0 hoặc x=1
5: =>2^x=32
=>x=5
6: =>(2x+1)^3=9^3
=>2x+1=9
=>2x=8
=>x=4
7: =>x^3=115
=>\(x=\sqrt[3]{115}\)
8: =>(2x-15)^5-(2x-15)^3=0
=>(2x-15)^3*[(2x-15)^2-1]=0
=>2x-15=0 hoặc (2x-15)^2-1=0
=>2x-15=0 hoặc 2x-15=1 hoặc 2x-15=-1
=>x=15/2 hoặc x=8 hoặc x=7
VN
Võ Ngọc Phương
VIP
2 tháng 8 2023
1. Tìm số tự nhiên x biết:
1) \(3^x.3=243\)
\(3^x=243:3\)
\(3^x=81\)
\(3^x=3^4\)
\(\Rightarrow x=4\)
_____
2) \(7.2^x=56\)
\(2^x=56:7\)
\(2^x=8\)
\(2^x=2^3\)
\(\Rightarrow x=3\)
_____
3) \(x^3=8\)
\(x^3=2^3\)
\(\Rightarrow x=3\)
_____
4) \(x^{20}=x\)
\(x^{20}-x=0\)
\(x\left(x^{19}-1\right)=0\)
\(\Rightarrow x=0\) hoặc \(x=1\)
5) \(2^x-15=17\)
\(2^x=17+15\)
\(2^x=32\)
\(2^x=2^5\)
\(\Rightarrow x=5\)
_____
6) \(\left(2x+1\right)^3=9.81\)
\(\left(2x+1\right)^3=729=9^3\)
\(\rightarrow2x+1=9\)
\(2x=9-1\)
\(2x=8\)
\(x=8:2\)
\(\Rightarrow x=4\)
_____
7) \(x^6:x^3=125\)
\(x^3=125\)
\(x^3=5^3\)
\(\Rightarrow x=5\)
_____
8) \(\left(2x-15\right)^5=\left(2x-15\right)^3\)
\(\rightarrow\left(2x-15\right)^5-\left(2x-15\right)^3=0\)
\(\left(2x-15\right)^3.\left[\left(2x-15\right)^2-1\right]=0\)
\(\Leftrightarrow\left\{{}\begin{matrix}\left(2x-15\right)^3=0\\\left(2x-15\right)^2-1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{15}{2}\\x=7\\x=8\end{matrix}\right.\)
_____
9) \(3^{x+2}-5.3^x=36\)
\(3^x.\left(3^2-5\right)=36\)
\(3^x.\left(9-5\right)=36\)
\(3^x.4=36\)
\(3^x=36:4\)
\(3^x=9\)
\(3^x=3^2\)
\(\Rightarrow x=2\)
_____
10) \(7.4^{x-1}+4^{x+1}=23\)
\(\rightarrow7.4^{x-1}+4^{x-1}.4^2=23\)
\(4^{x-1}.\left(7+4^2\right)=23\)
\(4^{x-1}.\left(7+16\right)=23\)
\(4^{x-1}.23=23\)
\(4^{x-1}=23:23\)
\(4^{x-1}=1\)
\(4^{x-1}=4^1\)
\(\rightarrow x-1=0\)
\(x=0+1\)
\(\Rightarrow x=1\)
Chúc bạn học tốt
3.(4-x) - 2.(x-1) = x + 20
<=> 12 - 3x - 2x + 2 = x + 20
<=> -6x = 6
<=> x = -1
4.(2x+7) - 3( 3x - 2 ) = 24
<=> 8x + 28 - 9x + 6 = 24
<=> -x = -10
<=> x = 10
3(x-2) + 2x = 10
<=> 3x - 6 + 2x = 10
<=> 5x = 16
<=> x = \(\frac{16}{5}\)
a, 3( 4-x) - 2(x-1) = x + 20
12 - 3x - 2x -2 = x + 20
10 - x = x + 20
=> 2x = 10 -(+20)
2x = 10 - 20
2x = -10
=> x = -10 : 2
=> x = -5
Vậy x = -5
b, 4(2x + 7) - 3(3x - 2) = 24
8x + 28 - 9x -9 = 24
=> -x + 19 = 24
-x = 24 - 19
=> -x = 5
=> x = -5
Vậy x = -5
c, 3(x - 2) + 2x = 10
3x - 6 + 2x = 10
5x - 6 = 10
5x = 10 + 6
5x = 16
=> x = \(\frac{16}{5}\)
Vậy x = \(\frac{16}{5}\)