a,\(3^2x-1=243\)

\(9x-1=243\)

\(9x=244\)

\(x=\frac{244}{9}\)

b,\(3^x+1=3^{2x}\)

\(x+1=2x\)

\(x-2x=-1\)

\(-1x=-1\)

\(x=1\)

Mình chỉ làm được 2 câu thôi chúc cậu học tốt!

a) \(3^{2x-1}=243\)

\(\Rightarrow3^{2x-1}=3^5\)

\(\Rightarrow2x-1=5\)

\(\Rightarrow2x=5+1\)

\(\Rightarrow2x=6\)

\(\Rightarrow x=6:2\)

\(\Rightarrow x=3\)

Vậy \(x=3.\)

b) \(3^{x+1}=9^x\)

Vậy \(x=1.\)

c) \(\left(\frac{4}{7}-\frac{1}{2}x\right)^3=-\frac{8}{34}\)

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Chúc bạn học tốt!

a) \(3^{2x-1}=243\)

\(\Leftrightarrow3^{2x-1}=3^5\)

\(\Leftrightarrow2x-1=5\)

\(\Leftrightarrow2x=5+1\)

\(\Leftrightarrow2x=6\)

\(\Leftrightarrow x=\dfrac{6}{2}\)

\(\Leftrightarrow x=3\)

Vậy \(x=3\)

b) \(\left(3^x\right)^2:3^3=\dfrac{1}{243}\)

\(\Leftrightarrow3^{2x}:3^3=\dfrac{1}{3^5}\)

\(\Leftrightarrow3^{2x}:3^3=3^{-5}\)

\(\Leftrightarrow3^{2x-3}=3^{-5}\)

\(\Leftrightarrow2x-3=-5\)

\(\Leftrightarrow2x=-5+3\)

\(\Leftrightarrow2x=-2\)

\(\Leftrightarrow x=-\dfrac{2}{2}\)

\(\Leftrightarrow x=1\)

Vậy \(x=1\)

c) \(2^{3x+2}=4^{x+5}\)

\(\Leftrightarrow2^{3x+2}=\left(2^2\right)^{x+5}\)

\(\Leftrightarrow2^{3x+2}=2^{2\left(x+5\right)}\)

\(\Leftrightarrow3x+2=2\left(x+5\right)\)

\(\Leftrightarrow3x+2=2x+10\)

\(\Leftrightarrow3x-2x=10-2\)

\(\Leftrightarrow x=8\)

Vậy \(x=8\)

d) \(3^{x+1}=9^x\)

\(\Leftrightarrow3^{x+1}=\left(3^2\right)^x\)

\(\Leftrightarrow3^{x+1}=3^{2x}\)

\(\Leftrightarrow x+1=2x\)

\(\Leftrightarrow2x-x=1\)

\(\Leftrightarrow x=1\)

Vậy \(x=1\)

1) \(\left(x-2\right)^2=1\)

\(\Leftrightarrow\left(x-2\right)^2=1^2\)

\(\Leftrightarrow\orbr{\begin{cases}x-2=1\\x-2=-1\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=3\\x=1\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}x=3\\x=1\end{cases}}\)

2) \(\left(2x-1\right)^3=-8\)

\(\Leftrightarrow\left(2x-1\right)^3=\left(-2\right)^3\)

\(\Leftrightarrow2x-1=-2\)

\(\Leftrightarrow2x=-2+1\)

\(\Leftrightarrow2x=-1\)

\(\Rightarrow x=-\frac{1}{2}\)

3) \(\left(x-1\right)^{x+2}=\left(x-1\right)^{x+4}\)

\(\Leftrightarrow x+2=x+4\)

\(\Leftrightarrow2=4\)

\(\Rightarrow x\in\varnothing\)

4) \(\left(2x-3\right)^5=-243\)

\(\Leftrightarrow\left(2x-3\right)^5=\left(-3\right)^5\)

\(\Leftrightarrow2x-3=-3\)

\(\Leftrightarrow2x=-3+3\)

\(\Leftrightarrow2x=0\)

\(\Rightarrow x=0\)

\(\left(x-2\right)^2=1\)

\(=>\left(x-2\right).\left(x-2\right)=1\)

\(+TH1\)\(\left(x-2\right)=1\)

\(=>1.1=1\left(TM\right)\)

\(+TH2\)\(\left(x-2\right)=-1\)

\(=>\left(-1\right).\left(-1\right)=1\left(TM\right)\)

\(=>x=1;-1\)

a: 3^x=243

=>3^x=3^5

=>x=5

b: 4^x=4096

=>4^x=4^5

=>x=5

c: 5^3-x=25

=>3-x=2

=>x=1

d: =>2x-3=3

=>2x=6

=>x=3

j: =>2^x*8+2^x*2=80

=>2^x=8

=>x=3

a: =>1/3x-2/5x=5

=>-1/15x=5

=>x=-75
b: =>4x=4

=>x=1

c: =>6*3^x-5*3^x=243

=>3^x=243

=>x=5

\(\left(x-2\right)^2=1\)

=> \(\left(x-2\right)^2=1^2\)

=> \(\left(x-2\right)^2=\left(-1\right)^2\)

=> \(\left[{}\begin{matrix}x-2=1\\x-2=-1\end{matrix}\right.\) => \(\left[{}\begin{matrix}x=1+2\\x=\left(-1\right)+2\end{matrix}\right.\)

=> \(\left[{}\begin{matrix}x=3\\x=1\end{matrix}\right.\)

Vậy \(x\in\left\{3;1\right\}.\)

\(\left(2x-1\right)^3=-8\)

=> \(\left(2x-1\right)^3=\left(-2\right)^3\)

=> \(2x-1=-2\)

=> \(2x=\left(-2\right)+1\)

=> \(2x=-1\)

=> \(x=\left(-1\right):2\)

=> \(x=-\frac{1}{2}\)

Vậy \(x=-\frac{1}{2}.\)

\(\left(2x-3\right)^5=-243\)

=> \(\left(2x-3\right)^5=\left(-3\right)^5\)

=> \(2x-3=-3\)

=> \(2x=\left(-3\right)+3\)

=> \(2x=0\)

=> \(x=0:2\)

=> \(x=0\)

Vậy \(x=0.\)

Chúc bạn học tốt!

a) (x - 2)² = 1

=> x - 2 = 1 hoặc x - 2 = -1

x = 3 ; x = 1

Vậy x = 3; x = 1

b) (2x - 1)³ = -8

=> 2x - 1 = -2

2x = -1

x = \(\frac{-1}{2}\)

Vậy x = \(\frac{-1}{2}\)

c) (2x - 3)⁵ = -243

=> (2x - 3)⁵ = (-3)⁵

=> 2x - 3 = -3

2x = 0

x = 0

Vậy x = 0

\(\frac{1}{3}\left(2x-\frac{1}{2}\right)^4=\frac{1}{243}\)

=> \(\left(2x-\frac{1}{2}\right)^4=\frac{1}{243}:\frac{1}{3}=\frac{1}{243}\cdot3=\frac{1}{81}\)

=> \(\left(2x-\frac{1}{2}\right)^4=\left(\pm\frac{1}{3}\right)^4\)

=> \(\hept{\begin{cases}2x-\frac{1}{2}=\frac{1}{3}\\2x-\frac{1}{2}=-\frac{1}{3}\end{cases}}\Rightarrow\hept{\begin{cases}x=\frac{5}{12}\\x=\frac{1}{12}\end{cases}}\)

(2x-1/2)^4=1/243:1/3

(2x-1/2)=1/243×3/1

(2x-1/2)^4=1/81

(2x-1/2)^4=1/3^4

(2x-1/2)=1/3

2x=1/3+1/2

2x=5/6

x=5/6:2/1

x=5/6×1/2

x=5/12

a: =>|x-4|=3-2x

\(\Leftrightarrow\left\{{}\begin{matrix}x< =\dfrac{3}{2}\\\left(3-2x-x+4\right)\left(3-2x+x-4\right)=0\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x< =\dfrac{3}{2}\\\left(-3x+7\right)\left(-x-1\right)=0\end{matrix}\right.\Leftrightarrow x=-1\)

b: =>x-1=-3

=>x=-2

a, 2³ + 2 = 4^x + 5

8 + 2 = 4^x + 5

10 = 4^x + 5

=> 4^x = 5

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