\(5.5^{2x+2}=125\)

\(=>5^{2x+2}=125:5\)

\(=>5^{2x+2}=25=5^2\)

\(=>2x+2=2\)

\(=>2x=2-2\)

\(=>2x=0\)

\(=>x=0:2\)

\(=>x=0\)

5 . 5^{2x + 2} = 125

5^{2x + 2} = 125 : 5

5^{2x + 2} = 25

5^{2x + 2} = 5² (cùng cơ số)

⇒ 2x + 2 = 2 hoặc 2x + 2 = -2

    2x = 2 - 2           2x = -2 - 2

    2x = 0                2x = -4

     x = 0                   x = -4 : 2

                                x = -2

Vậy x = 0 hoặc -2.

Đáp án đúng : C

\(1+5^2+5^4+...+5^{2x}\left(1\right)=\dfrac{25^6-1}{24}\)

Đặt \(\left(1\right)=A\)

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

\(\Rightarrow5^2A=5^2+5^4+...+5^{2x+2}\)

\(\Rightarrow25A=5^2+5^4+...+5^{2x+2}\)

\(\Rightarrow25A-A=5^2+5^4+...+5^{2x+2}-1-5^2-...-5^{2x}\)

\(\Rightarrow24A=5^{2x+2}-1\)

\(\Rightarrow A=\dfrac{5^{2x+2}-1}{24}\)

Mà: \(A=\dfrac{25^6-1}{24}\)

\(\Rightarrow\dfrac{5^{2x+2}-1}{24}=\dfrac{\left(5^2\right)^6-1}{24}\)

\(\Rightarrow5^{2x+2}-1=5^{12}-1\)

\(\Rightarrow5^{2x+2}=5^{12}\)

\(\Rightarrow2x+2=12\)

\(\Rightarrow2x=10\)

\(\Rightarrow x=\dfrac{10}{2}\)

\(\Rightarrow x=5\)

a, \(x+45=54\Leftrightarrow x=9\)

b, \(x+9=3\Leftrightarrow x=-6\)

c, \(5^{2x}=5^2\Rightarrow2x=2\Leftrightarrow x=1\)

\(a,\left(x+45\right)-54=0\\ \Rightarrow x+45=54\\ \Rightarrow x=9\\ b,12\left(x+9\right)=36\\ \Rightarrow x+9=3\\ \Rightarrow x=-6\\ c,5^{2x}=25\\ \Rightarrow5^{2x}=5^2\\ \Rightarrow2x=2\\ \Rightarrow x=1\)

a)x+45=54=>x=9

b)x+9=3=>x=-6

c)x=1

Chúc em học tốt

a). 5^x = 125

=>5^x = 5³

=> x = 3

b) 3^2x = 81

=> 3^2x = 3⁴

=> 2x = 4

=> x = 2

c). 5^2x-3 – 2.5² = 5² .3

=>5^2x: 5³ = 5² .3 + 2.5²

=>5^2x: 5³ = 5² .5

=>
5^2x = 5² .5.5³

=>5^2x = 5⁶

=> 2x = 6

=> x=3

a) 5x = 125

x = 125 : 5

x = 25

b) 32x = 81

x = 81 : 32

x = 81/ 32

c) 52x - 3 - 2.52 = 52.3

52x - 3 - 104 = 156

x - 3 - 104 = 156 : 52

x - 3 - 104 = 3

x - 3 = 3 + 104

x - 3 = 107

x = 107 + 3

x = 110

Ko chắc lắm , sai thì Sorry nhé .

\(a,\\ 5x=125\\ < =>x=125:5\\ < =>x=25\)

\(b,\\ 32x=81\\ < =>x=81:32\\ < =>x=\frac{81}{32}\)

\(c,\\ 52x-3-2.52=52.3\\ < =>52x-3-104=156\\ < =>52x-107=156\\ < =>52x=156+107\\ < =>52x=263\\ < =>x=x=\frac{263}{52}\)

Ta có: \(100< 5^{2x-1}\le5^6\)

\(\Leftrightarrow5^2< 5^{2x-1}\le5^6\)

\(\Leftrightarrow2x-1\in\left\{3;5\right\}\)

\(\Leftrightarrow2x\in\left\{4;6\right\}\)

hay \(x\in\left\{2;3\right\}\)

Ta có: 100 < 52x – 1 < 56

=> 52 < 100 < 52x-1 < 56

=> 2 < 2x – 1 < 6

=> 2 + 1 < 2x < 6 + 1

=> 3 < 2x < 7

Vì x ∈ N nên suy ra: x ∈ {2; 3} là thỏa mãn.

Ta có 100=5².4

\(\Rightarrow5^3\le5^{2x-1}< 5^6\)

\(\Rightarrow3\le2x-1< 6\)

\(\Rightarrow4\le2x< 7\)

\(\Rightarrow2\le x< 3,5\)

Mà \(x\) là số tự nhiên

\(\Rightarrow x=2\) hoặc \(x=3\)

x ϵ {2;3}