Question

Tìm x, biết rằng:

1) ( 2x + 1)³ = -0,001

2) ( 2x -3 )⁴ = ( 2x-3 )⁶

3) ( 2x+1 )⁵ = ( 2x+1)²⁰¹⁰

4) \(\dfrac{8}{25}=\dfrac{2^x}{5^{x-1}}\)

5) 9^x : 3^x = 3

6) \(3^x+3^{x+3}=756\)

7) \(5^{x+1}+6.5^{x+1}=875\)

8) \(2^{x-1}.3^{y+1}=12^{x+9}\)

9) \(3^x=9^{y-1}\)

10) \(2^{x+1}.5^y=20^x\)

11) 15^x : 3^y = 75^y

12) \(\dfrac{3}{5}:\dfrac{2x}{15}=\dfrac{1}{2}:\dfrac{4}{5}\)

13) \(\dfrac{x}{2}=\dfrac{y}{3}=\dfrac{z}{4}\) và xy + yz + zx = 104

Answer 1

1,

\(\left(2x+1\right)^3=-0,001\\ \left(2x+1\right)^3=\left(-0.1\right)^3\\ \Leftrightarrow2x+1=-0.1\\ 2x=-1.1\\ x=-\dfrac{11}{10}:2\\ x=-\dfrac{11}{20}\\ Vậy...\)

2,

\(\left(2x-3\right)^4=\left(2x-3\right)^6\\ \Leftrightarrow\left(2x-3\right)^6-\left(2x-3\right)^4=0\\ \Leftrightarrow\left(2x-3\right)^4\cdot\left[\left(2x-3\right)^2-1\right]=0\\ \Rightarrow\left\{{}\begin{matrix}\left(2x-3\right)^4=0\\\left(2x-3\right)^2-1=0\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}2x-3=0\\\left(2x-3\right)^2=1\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}2x=3\\2x-3=1\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{3}{2}\\x=2\end{matrix}\right.\\ Vậyx\in\left\{\dfrac{3}{2};2\right\}\)

3, Làm tương tự câu 2

5,

\(9^x:3^x=3\\ \left(9:3\right)^x=3\\ 3^x=3\\ \Rightarrow x=1\\ Vậy...\)

6,

\(3^x+3^{x+3}=756\\ 3^x+3^x\cdot3^3\\ 3^x\cdot\left(1+27\right)=756\\ 3^x\cdot28=756\\ \Leftrightarrow3^x=27\\ 3^x=3^3\\ \Rightarrow x=3\\ vậy...\)

7,

\(5^{x+1}+6\cdot5^{x+1}=875\\ 5^{x+1}\cdot\left(1+6\right)=875\\ 5^{x+1}\cdot7=875\\ \Leftrightarrow5^{x+1}=125\\ \Leftrightarrow5^{x+1}=5^3\Leftrightarrow x+1=3\\ \Rightarrow x=2\\ Vậy...\)

9,