x^5=625.x 

<=>x^5:x=625

<=>x^4=625

<=>x^4=5^4

<=>x=5

\(5^{x+2}+5^{x+1}+5^x=5^x\left(5^2+5+1\right)=5^x.31=19375\)

=>5^x=625=>x=4

5^x + 2 + 5^x + 1 + 5^x = 19375

3 * 5^x + 3 = 19375

3 * 5^x = 19372

5^x = 

5^x+2+5^x+1+5^x=19375

⇒ ( 5^x .5²) +(5^x .5) +5^x= 19375

⇒ 5^x (25+5+1)=19375

⇒ 31. 5^x = 19375

⇒ 5^x = 625

⇒5^x=5⁴

⇒x=4

a,

\(\dfrac{5^x}{125}=5^4\\ 5^x:5^3=5^4\\ 5^x=5^4\cdot5^3\\ 5^x=5^7\\ \Rightarrow x=7\)

b,

\(\dfrac{3^x}{3}+3^{x-2}=4\\ 3^{x-1}+3^{x-2}=3^1+3^0\\ \Rightarrow x=2\)

c,

\(\left(x+\dfrac{2006}{2007}\right)^6=0\\ \Rightarrow x+\dfrac{2006}{2007}=0\\ x=0-\dfrac{2006}{2007}\\ x=\dfrac{-2006}{2007}\)

d,

\(\left(x-\dfrac{1}{5}\right)^3=\dfrac{8}{125}\\ \left(x-\dfrac{1}{5}\right)^3=\left(\dfrac{2}{5}\right)^3\\ \Rightarrow x-\dfrac{1}{5}=\dfrac{2}{5}\\ x=\dfrac{2}{5}+\dfrac{1}{5}\\ x=\dfrac{3}{5}\)

e,

\(3^x+3^{x-2}=810\\ 3^x\left(1+3^2\right)=810\\ 3^x\cdot10=810\\ 3^x=810:10\\ 3^x=81\\ 3^x=3^4\\ \Rightarrow x=4\)

g,

\(5^{x+2}+5^{x+1}+5^x=19375\\ 5^x\left(5^2+5+1\right)=19375\\ 5^x\cdot31=19375\\ 5^x=19375:31\\ 5^x=625\\ 5^x=5^4\\ \Rightarrow x=4\)

sao đây đề dễ mà bên kia làm ko đc 1 bài haizzzzzzz

a) \(5^{x-1}+5^{x-3}=650\)

\(\Rightarrow5^x\left(\frac{1}{5}+\frac{1}{125}\right)=650\)

\(\Rightarrow5^x=650:\frac{26}{125}\)

\(\Rightarrow5^x=3125\)

\(\Rightarrow5^x=5^5\)

\(\Rightarrow x=5\)