\(10^x.5^y=20^y\)

=> \(2^x.5^{x+y}=\left(2^2.5\right)^y\)

=> \(2^x.5^{x+y}=2^{2y}.5^y\)

=> x = 2y; x + y = y

=> 2y + y = y

=> 3y = y

=> 2y = 0

=> y = 0 => x = 2y = 0

Vậy x = y = 0.

x=y=0

25.(x-590.5+2)=75

25.(x - 590.5 + 2) = 75

=> x - 2950 + 2 = 3

=> x - 2948 = 3

=> x = 2951

25 x (X - 590 x 5 + 2) = 75

       (X - 590 x 5 + 2) = 75 : 25

       (X - 590 x 5 + 2) = 3

           (X - 2950 + 2) = 3

           X - (2950 - 2)  = 3

                    X - 2948 = 3

                               X = 3 + 2948

                               X = 2951

b) Ta có: \(-5+\left|3x-1\right|+6=\left|-4\right|\)

\(\Leftrightarrow\left|3x+1\right|+1=4\)

\(\Leftrightarrow\left|3x+1\right|=3\)

\(\Leftrightarrow\left[{}\begin{matrix}3x+1=3\\3x+1=-3\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}3x=2\\3x=-4\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{2}{3}\\x=-\dfrac{4}{3}\end{matrix}\right.\)

Vậy: \(x\in\left\{\dfrac{2}{3};-\dfrac{4}{3}\right\}\)

c) Ta có: \(\left(x-1\right)^2=\left(x-1\right)^4\)

\(\Leftrightarrow\left(x-1\right)^2-\left(x-1\right)^4=0\)

\(\Leftrightarrow\left(x-1\right)^4-\left(x-1\right)^2=0\)

\(\Leftrightarrow\left(x-1\right)^2\cdot\left[\left(x-1\right)^2-1\right]=0\)

\(\Leftrightarrow\left(x-1\right)^2\cdot\left(x-1-1\right)\left(x-1+1\right)=0\)

\(\Leftrightarrow x\cdot\left(x-1\right)^2\cdot\left(x-2\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=0\\\left(x-1\right)^2=0\\x-2=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x-1=0\\x-2=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=1\\x=2\end{matrix}\right.\)

Vậy: \(x\in\left\{0;1;2\right\}\)

d) Ta có: \(5^{-1}\cdot25^x=125\)

\(\Leftrightarrow5^{-1}\cdot5^{2x}=5^3\)

\(\Leftrightarrow5^{2x-1}=5^3\)

\(\Leftrightarrow2x-1=3\)

\(\Leftrightarrow2x=4\)

hay x=2

Vậy: x=2

\(5^{-1}.25^x=125\)

\(-5.25^x=125\)

\(25^x=125:\left(-5\right)\)

\(25^x=-25\)

\(\Rightarrow x=-1\)

minh bik lam bai b thui a

25^x=5^2.x:5^1.x+y=5^3

suy ra 2.x : 1.x+y=3

a)\(\frac{27^x}{3^{x-y}}=243\)

\(\Rightarrow\frac{3^3^x}{3^x:3^y}=243\)

\(\Rightarrow\frac{3^{3x}}{3^x}.3^y=243\)

\(\Rightarrow3^{2x}.3^y=243\)

\(\Rightarrow3^{2x+y}=3^5\)

\(\Rightarrow2x+y=5\) (1)

b) \(\frac{25^x}{5^x.5^y}=125\)

\(\Rightarrow\frac{5^{2x}}{5^x}.\frac{1}{5^y}=5^3\)

\(\Rightarrow\frac{5^x}{5^y}=5^3\)

\(\Rightarrow5^{x-y}=5^3\Rightarrow x-y=3\) (2)

Từ (1) và (2) ta có :

2x+y = 5 và x-y=3

 * 2x +y = 5 => x = \(\frac{5-y}{2}\) .Thay x = \(\frac{5-y}{2}\) vào x - y =3

\(\Rightarrow\frac{5-y}{2}-y=3\) \(\Rightarrow\frac{5-y}{2}-\frac{2y}{2}=3\Rightarrow\frac{5-y-2y}{2}=3\Rightarrow5-3y=6\) \(\Rightarrow5-6=3y\Rightarrow-1=3y\Rightarrow y=\frac{-1}{3}\)

Thế  y = -1/3 vào x - y =3 .Ta có : \(x-\frac{-1}{3}=3\Rightarrow x+\frac{1}{3}=3\Rightarrow x=3-\frac{1}{3}=\frac{8}{3}\)

Vậy : x=8/3 và y = -1/3

a)Câu a sai đề

b)x=4

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