( 5/4 ) ^2x+ 7 = ( 5/4 )^4

=> 2x + 7 = 4

=> 2x       = -3

x            = -3/2

xem lại 5/4 hay 4/5

Để sai rồi : 

\(\left(\frac{5}{4}\right)^{2x+7}=\frac{625}{256}\)

\(\Leftrightarrow\left(\frac{5}{4}\right)^{2x+7}=\left(\frac{5}{4}\right)^4\)

<=> 2x + 7 = 4

<=> 2x = -3

<=> x = -3/2

Vậy x = -3/2

\(\left(\frac{5}{4}\right)^{2x+7}\Leftrightarrow\left(\frac{5}{4}\right)^4\)

suy ra 2x+7=4

         2x     =-3

          x       = -3/2

a: =>2x+5=4

=>2x=-1

hay x=-1/2

b: \(\Leftrightarrow\left(3x-4\right)^2\cdot\left[\left(3x-4\right)^2-1\right]=0\)

=>(3x-4)(3x-5)(3x-3)=0

hay \(x\in\left\{1;\dfrac{4}{3};\dfrac{5}{3}\right\}\)

c: \(\Leftrightarrow3^{x+1}=3^{2x}\)

=>2x=x+1

=>x=1

d: \(\Leftrightarrow2^{2x+3}=2^{2x-10}\)

=>2x+3=2x-10

=>0x=-13(vô lý)

256/625=(4/5)⁴

=>2x+7=4

2x=-3

x=-3/2

a: \(\Leftrightarrow2x+7=-4\)

=>2x=-11

hay x=-11/2

b: \(\Leftrightarrow\dfrac{7^x\cdot49+7^x\cdot7+7^x}{57}=\dfrac{5^{2x}+5^{2x+1}+5^{2x+3}}{131}\)

\(\Leftrightarrow7^x=5^{2x}\)

=>x=0

a) \(\left(x-4\right)^2=\left(x-4\right)^4\)

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

\(\Rightarrow\left(x-4\right)^2.\left[1-\left(x-4\right)^2\right]=0\)

\(\Rightarrow\left[{}\begin{matrix}\left(x-4\right)^2=0\\1-\left(x-4\right)^2=0\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x-4=0\\\left(x-4\right)^2=1^2\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x-4=0\\x-4=1\\x-4=-1\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x=4\\x=5\\x=3\end{matrix}\right.\)

dùng "tích trung tỉ bằng tích ngoại tỉ"