đáp án :2

a)    9^x-1=3²

( 3² )^x-1 = 3²

 3^2x-2    = 3²

⇒ 2x-2 = 2

    2x    = 2+2

    2x    = 4

   x       = 4 : 2

   x       = 2

b) 5^x+2=625

    5^x+2= 5⁴

⇒ x+2 = 4

    x     = 4-2

   x      = 2

c) 2^x: 2⁵= 2

    2^x:2⁵ = 2¹

    2^x      = 2¹ . 2⁵

    2^x      = 2⁶

⇒ x        = 6

d) 3^x:27=3

    3^x:3³ = 3¹

     3^x     = 3¹.3³

    3^x     = 3⁴

⇒ x      = 4

a) Ta có: \(9^{x-1}=3^2\)

\(\Leftrightarrow3^{2x-2}=3^2\)

\(\Leftrightarrow2x-2=2\)

\(\Leftrightarrow2x=4\)

hay x=2

Vậy: x=2

b) Ta có: \(5^{x+2}=625\)

\(\Leftrightarrow5^{x+2}=5^4\)

\(\Leftrightarrow x+2=4\)

hay x=2

Vậy: x=2

c) Ta có: \(2^x:2^5=2\)

\(\Leftrightarrow2^{x-5}=2^1\)

\(\Leftrightarrow x-5=1\)

hay x=6

Vậy: x=6

d) Ta có: \(3^x:27=3\)

\(\Leftrightarrow3^x:3^3=3\)

\(\Leftrightarrow3^{x-3}=3^1\)

\(\Leftrightarrow x-3=1\)

hay x=4

Vậy: x=4

60  2         84  2      215  3     400  2

30  2         42  2       75   3      200  2

15  3         21  3       25   5       100  2

5  5           7   7        5     5        50  2

1                 1           1                25  5

                                                    5  5

                                                     1

máy không ghi dấu gạch được nên thông cảm

học tốt nhé!

a, 7x + 10x  = 5x 

    17x = 5x

17x - 5x = 0

      12x = 0

          x =0

2; 

a, 4x + 7x = 22

    11x = 22

        x = 2

b, 12x - 8x = 25

     4x = 25

       x = \(\dfrac{25}{4}\)

c,  \(\dfrac{1}{2}\)x - \(\dfrac{1}{3}\)x = \(\dfrac{4}{5}\) 

     (\(\dfrac{1}{2}-\dfrac{1}{3}\))x = \(\dfrac{4}{5}\)

    \(\dfrac{1}{6}\)x     = \(\dfrac{4}{5}\) 

      x = \(\dfrac{4}{5}\) : \(\dfrac{1}{6}\)

     x = \(\dfrac{24}{5}\)

\(\left(x+2\right)-2=0\)

\(\Rightarrow x+2-2=0\)

\(\Rightarrow x=0\)

\(\left(x+3\right)+1=7\)

\(\Rightarrow x+3+1=7\)

\(\Rightarrow x+4=7\)

\(\Rightarrow x=3\)

\(\left(3x-4\right)+4=12\)
\(\Rightarrow3x-4+4=12\)

\(\Rightarrow3x=12\)

\(\Rightarrow x=4\)

\(\left(5x+4\right)-1=13\)

\(\Rightarrow5x+4-1=13\)

\(\Rightarrow5x+3=13\)

\(\Rightarrow5x=10\)

\(\Rightarrow x=2\)

\(\left(4x-8\right)-3=5\)

\(\Rightarrow4x-8-3=5\)

\(\Rightarrow4x-11=5\)

\(\Rightarrow4x=16\)

\(\Rightarrow x=4\)

\(8-\left(2x+4\right)=2\)

\(\Rightarrow8-2x-4=2\)

\(\Rightarrow4-2x=2\)

\(\Rightarrow2x=2\)

\(\Rightarrow x=1\)

\(7+\left(5x+2\right)=14\)

\(\Rightarrow7+5x+2=14\)

\(\Rightarrow9+5x=14\)

\(\Rightarrow5x=5\)

\(\Rightarrow x=1\)

\(5-\left(3x-11\right)=1\)

\(\Rightarrow5-3x+11=1\)

\(\Rightarrow16-3x=1\)

\(\Rightarrow3x=15\)

\(\Rightarrow x=5\)

\(a,\Leftrightarrow x-28=-45\\ \Leftrightarrow x=-27\\ b,\Leftrightarrow3+x=0\\ \Leftrightarrow x=-3\\ c,\Leftrightarrow\left[{}\begin{matrix}7-x=0\\-x+2=0\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=7\\x=-2\end{matrix}\right.\\ d,\Leftrightarrow16\left(x^2-4\right)=0\\ \Leftrightarrow\left(x-2\right)\left(x+2\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x-2=0\\x+2=0\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=2\\x=-2\end{matrix}\right.\)

a)-28+x=-34+(-11)             b)-12(3+x)=0

<=>-28+x=-45                   <=>-36-12x=0

<=>x=-17                            <=>-12x=36

Vậy x=-17                             <=>x=-3

                                         Vậy x=-3

c)(7-x)(-x+2)=0

<=>7-x=0 hoặc -x+2=0

Th1:7-x=0                    Th2:-x+2=0

 <=>x=7                             <=>x=2

           Vậy xϵ{7;2}

d)16x2-64=0

<=>32x=64

<=>x=2

Vậy x=2

Ta có: \(\dfrac{-4}{15}< \dfrac{5x-1}{18}< \dfrac{5}{12}\)

\(\Leftrightarrow\dfrac{-48}{180}< \dfrac{10\left(5x-1\right)}{180}< \dfrac{75}{180}\)

Suy ra: \(-48< 10\left(5x-1\right)< 75\)

\(\Leftrightarrow10\left(5x-1\right)\in\left\{-40;-30;-20;-10;0;10;20;30;40;50;60;70\right\}\)

\(\Leftrightarrow5x-1\in\left\{-4;-3;-2;-1;0;1;2;3;4;5;6;7\right\}\)

\(\Leftrightarrow5x\in\left\{-3;-2;-1;0;1;2;3;4;5;6;7;8\right\}\)

\(\Leftrightarrow x\in\left\{0;1\right\}\)(Vì x nguyên)

a) \(B=5+5^2+5^3+...+5^{2022}\)

\(\Rightarrow5B=5^2+5^3+5^4+...+5^{2023}\)

\(\Rightarrow4B=5^{2023}-5\)

b) \(4B+5=5^X\)

Hay \(5^{2023}-5+5=5^X\)

\(5^{2023}=5^x\)

\(\Rightarrow x=2023\)

   B = 5 + 5² + 5³ +...+ 5²⁰²²

5.B =       5² + 5³ +....+ 5²⁰²³

5B- B =   5²⁰²³ - 5

4B     = 5²⁰²³ - 5

b, 4B + 5 = 5\(^x\) ⇒ 5²⁰²³ - 5 + 5 = 5\(^x\)

                           5\(^{2023}\)             = 5^\(x\)

                                  \(x\)                 = 2023

\(\left(x+15\right):3=7\)

\(x+15=7.3\)

\(x+15=21\)

\(x=21-15\)

\(x=6\)

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\(4.\left(6-x\right)=280:36\)

\(4.\left(6-x\right)=\dfrac{70}{9}\)

\(6-x=\dfrac{70}{9}:4\)

\(6-x=\dfrac{35}{18}\)

\(x=6-\dfrac{35}{18}\)

\(x=\dfrac{73}{18}\)

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\(5x-3x-12=8\)

\(2x=8+12\)

\(2x=20\)

\(x=\dfrac{20}{2}\)

\(x=10\)

\(\left(x+15\right):3=7\\ \Rightarrow x+15=7.3=21\\ \Rightarrow x=21-15=6\)

\(4\left(6-x\right)=280:36\\ \Rightarrow4\left(6-x\right)=\dfrac{70}{9}\\ \Rightarrow6-x=\dfrac{70}{9}:4\\ \Rightarrow6-x=\dfrac{35}{18}\\ \Rightarrow x=6-\dfrac{35}{18}=\dfrac{73}{18}\)

\(5x-3x-12=8\\ \Rightarrow2x=8+12=20\\ \Rightarrow x=\dfrac{20}{2}=10\)