a, \(5^x+5^{x+1}+5^{x-2}=151\)

\(\Rightarrow5^x.\left(1+5+5^{-2}\right)=151\)

\(\Rightarrow5^x.6,04=151\Rightarrow5^x=25=5^2\)

Vì \(5\ne-1;5\ne0;5\ne1\) nên \(x=2\)

b, \(5^{x-1}+5^{x-2}+5^{x-3}=155\)

\(\Rightarrow5^x.\left(5^{-1}+5^{-2}+5^{-3}\right)=155\)

\(\Rightarrow5^x.0,248=155\Rightarrow5^x=625=5^4\)

Vì \(5\ne-1;5\ne0;5\ne1\) nên \(x=4\)

\(•5^x+5^{x+1}+5^{x-2}=151\\ 5^x\left(1+5+\dfrac{1}{25}\right)=151\\ 5^x=25\\ \Rightarrow x=2\)

\(•5^{x-1}+5^{x-2}+5^{x-3}=155\\ 5^x.\left(\dfrac{1}{5}+\dfrac{1}{25}+\dfrac{1}{125}\right)=155\\ 5^x=625\\ \Rightarrow x=4\)

\(•5^{2+x}+5^{3+x}=750\\ 5^x\left(25+125\right)=750\\ 5^x=5\\ \Rightarrow x=1\)

\(5^{x+1}+5^{x+2}=750\)

\(\Rightarrow5^{x+1}\left(1+5\right)=750\)

\(\Rightarrow5^{x+1}.6=750\Rightarrow5^{x+1}=125\)

\(\Rightarrow5^{x+1}=5^3\)

\(\Rightarrow x+1=3\Rightarrow x=2\)

\(5^{x+1}+5^{x+2}=750\)

\(\Rightarrow5^x.5+5^x.5^2=750\)

\(\Rightarrow5^x.5+5^x.25=750\)

\(\Rightarrow5^x\left(5+25\right)=750\)

\(\Rightarrow5^x.30=750\)

\(\Rightarrow5^x=25\)

\(\Rightarrow x=2\)

Đề có sai sót chỗ nào k v bạn

Nhấn vào "Đúng 0" thì lời giải sẽ hiện ra

\(5^{x+1}+5^{x+2}=750\)

\(5^x.5+5^x.5^2=750\)

\(5^x.5+5^x.25=750\)

\(5^x.\left(5+25\right)=750\)

\(5^x.30=750\)

\(5^x=750:30\)

\(5^x=25\)

\(5^x=5^2\)

\(\Rightarrow x=2\)

\(5^{x+1}+5^{x+2}=750\)

\(\Rightarrow5^x\times5+5^x\times5^2=750\)

\(\Rightarrow5^x\times\left(5+5^2\right)=750\)

\(\Rightarrow5^x\times30=750\)

\(\Rightarrow5^x=750:30\)

\(\Rightarrow5^x=25\)

\(\Rightarrow5^x=5^2\)

\(\Rightarrow x=2\)

Vậy x = 2

_Chúc bạn học tốt_

( x + 1 ) + ( x + 2 ) + ... + ( x + 9 ) = 750

9x + 45 = 750

9x = 750 - 45

9x = 705

x = 705 : 9

x = 78,33333333333333333333333....

Ta có:(x+1)+(x+2)+(x+3)+(x+4)+...+(x+9)=750

    suy ra:(x+x+x+x+x+x+x+x+x)+(1+2+...+9)=750

    suy ra:9.x+(9+1).9:2=750

   suy ra:9x+45=750

  suy ra:9x=705

 suy ra x =705/9

nhớ bấm đúng cho mình nha

X x 9 + ( 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 ) = 750

X x9 +                         45                          = 750

X x 9                                                        = 750-45

X x 9                                                        = 705

X                                                             = 705 : 9

X                                                             = 705/9

Ta có \(5^x+5^{x+1}=750\)

\(\Rightarrow5^x+5^x.5=750\)

\(\Rightarrow5^x.\left(1+5\right)=750\)

\(\Rightarrow5^x.6=750\)

\(\Rightarrow5^x=125\)

\(\Rightarrow5^x=5^3\)

\(\Rightarrow x=3\)

\(5^x\) +  \(5^{x+1}\) =  \(750\)

=> \(5^x\) + \(5^x\) . \(5\)= \(750\)

=> \(5^x\). \(\left(1+5\right)\)=\(750\)

=> \(5^x\). \(6\)= \(750\)

=>        \(5^x\)= \(125\)

=>         \(5^x\) = \(5^3\)

=>         \(x=3\)

Có \(5^x+5^{x+1}=750\)

=> \(5^x\left(1+5\right)=750\)

=> \(5^x=\frac{750}{6}=125\)

=> \(x=3\) 

Hok tốt nhen ^_^

\(x=3\)

học tốt

\(5^{x+1}+5^{x+2}=750\)

\(\Leftrightarrow5^x.5^1+5^x.5^2=750\)

\(\Leftrightarrow5^x.5+5^x.25=750\)

\(\Leftrightarrow5^x.\left(5+25\right)=750\)

\(\Leftrightarrow5^x.30=750\)

\(\Leftrightarrow5^x=750:30\)

\(\Leftrightarrow5^x=25\)

\(\Leftrightarrow5^x=5^2\)

\(\Rightarrow x=2\)

5^{x + 1} + 5^{x + 2} = 750

=> 5^x . 5 + 5^x . 5² = 750

=> 5^x . (5 + 5²) = 750

=> 5^x . (5 + 25) = 750

=> 5^x . 30 = 750

=> 5^x = 750 : 30

=> 5^x = 25

=> 5^x = 5²

=> x = 2

Vậy x = 2

\(5^{x+1}+5^{x+2}=750.\)

\(5^x.5+5^x.5^2=750\)

\(5^x.\left(5+5^2\right)=750\)

\(5^x.\left(5+25\right)=750\)

\(5^x.30=750\)

\(5^x=750:30\)

\(5^x=25\)

\(\Rightarrow x=2\)