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\(a,\Rightarrow\left(x-\dfrac{1}{2}\right)^3=\dfrac{1}{27}=\left(\dfrac{1}{3}\right)^3\\ \Rightarrow x-\dfrac{1}{2}=\dfrac{1}{3}\Rightarrow x=\dfrac{5}{6}\\ b,\Rightarrow\left(\dfrac{3}{2}\right)^{2x-1}:\left(\dfrac{3}{2}\right)^9=\left(\dfrac{3}{2}\right)^4\\ \Rightarrow2x-1-9=4\\ \Rightarrow2x=14\Rightarrow x=7\\ c,\Rightarrow2^{x-1}+2^{x+2}=9\cdot2^5\\ \Rightarrow2^{x-1}\left(1+2^3\right)=9\cdot2^5\\ \Rightarrow2^{x-1}\cdot9=9\cdot2^5\\ \Rightarrow2^{x-1}=2^5\Rightarrow x-1=5\Rightarrow x=6\\ d,\Rightarrow\left(2x+1\right)^2=12+69=81\\ \Rightarrow\left[{}\begin{matrix}2x+1=9\\2x+1=-9\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=4\\x=-5\end{matrix}\right.\)
1. \(2^x=4^{y-1}\Rightarrow2^x=\left(2^2\right)^{y-1}=2^{2y-2}\Rightarrow x=2y-2\)
\(27^y=3^{x+8}\Rightarrow\left(3^3\right)^y=3^{x+8}\Rightarrow3^{3y}=3^{x+8}\Rightarrow3y=x+8\)
ta có: x=2y-2
mà 3y=x+8
=> 3y=2y-2+8
=> 3y-2y+2-8=0
=> y-6=0
=> y=6
x=2y-2
=> x=2.6-2=12-2=10
Vậy x=10; y=6.
2.a.\(\left(-\frac{1}{3}\right)^{n-5}=\frac{1}{81}\)
\(\Rightarrow \left(-\frac{1}{3}\right)^{n-5}=\left(-\frac{1}{3}\right)^4\)
=> n-5=4
=> n=4+5
=> n=9
b.\(2^{-1}.2^n+4.2^n=9.2^5\)
\(\Rightarrow2^n.\left(2^{-1}+4\right)=9.32\)
=> 2n.(2-1+4)=288
=> 2n.(1/2+4)=288
=> 2n.9/2=288
=> 2n=288:9/2
=> 2n=64
=> 2n=26
Vậy n=6.
1.
a) \(x\in\left\{4;5;6;7;8;9;10;11;12;13\right\}\)
b) x=0
d) \(x=\frac{-1}{35}\) hoặc \(x=\frac{-13}{35}\)
e) \(x=\frac{2}{3}\)
Mk làm lun, ko viết lại đề bài nữa nhé =))
a) \(\Leftrightarrow\)\(3^2.3^{n+1}=9^4\)
\(\Leftrightarrow3^{n+1}=9^4:3^2\)
\(\Leftrightarrow3^{n+1}=3^6\)
\(\Rightarrow n+1=6\)
\(\Leftrightarrow n=6-1\)
\(\Rightarrow n=5\)
b)\(\Leftrightarrow2^n.\left(\frac{1}{2}+4\right)=9.2^5\)
\(\Leftrightarrow2^n.\frac{9}{2}=9.2^5\)
\(\Rightarrow2^n=\left(9.2^5\right):\frac{9}{2}\)
\(\Rightarrow2^n=468:\frac{9}{2}\)
Tự tính nốt KQ giúp mk nha ♥
2^-1.2^x+4.2^x=9.2^5
0,5.2^x+4.2^x=288
2^x.(4+0,5)=288
2^x.4,5=288
2^x=288:4,5
2^x=64
2^x=2^6
=) x=6
a) Ta có: \(5x\left(\frac{1}{5}x-2\right)+3\left(6-\frac{1}{3}x^2\right)=12\)
\(\Leftrightarrow x^2-10x+18-x^2=12\)
\(\Leftrightarrow-10x+18=12\)
\(\Leftrightarrow-10x=-6\)
hay \(x=\frac{3}{5}\)
Vậy: \(x=\frac{3}{5}\)
b) Ta có: \(7x\left(x-2\right)-5\left(x-1\right)=7x^2+3\)
\(\Leftrightarrow7x^2-14x-5x+5-7x^2-3=0\)
\(\Leftrightarrow-19x+2=0\)
\(\Leftrightarrow-19x=-2\)
hay \(x=\frac{2}{19}\)
Vậy: \(x=\frac{2}{19}\)
a) 2-1.2x + 4.2x = 9.25
=> 2x-1 + 4.2.2x-1 = 9.25
=> 2x-1 + 8.2x-1 = 9.25
=> 2x-1.(1 + 8) = 9.25
=> 2x-1.9 = 9.25
=> x - 1 = 5
=> x = 5 + 1 = 6
Vậy x = 6
b) (7x + 2)-1 = \(\frac{1}{9}\)
=> 7x + 2 = 9
=> 7x = 9 - 2
=> 7x = 7
=> x = 7 : 7 = 1
Vậy x = 1
a) 2^(-1) . 2^x + 4 . 2^x = 9 . 2^5
=> 1/2 . 2^x + 4 . 2^x = 9 . 32
=> 2^x . (1/2 + 4) = 288
=> 2^x . 9/2 = 288
=> 2^x = 288 : 9/2
=> 2^x = 64
2^x = 2^6
=> x = 6
b) (7x + 2)^(-1) = 1/9
=> 1 phần 7x + 2 = 1/9
=> 7x + 2 = 9
=> 7x = 9 - 2
=> 7x = 7
=> x = 7 : 7
=> x = 1