\(\left(x-3\right):\left[\frac{1}{2}.\left(-1\frac{3}{4}\right)\right]=-2\frac{1}{2}\)

\(\left(x-3\right):\left[\frac{1}{2}.\left(\frac{-7}{4}\right)\right]=\frac{-5}{2}\)

\(\left(x-3\right):\frac{-7}{8}=\frac{-5}{2}\)

\(\left(x-3\right)=\frac{-5}{2}.\frac{-7}{8}\)

\(\left(x-3\right)=\frac{35}{16}\)

\(x=\frac{35}{16}+3=\frac{83}{16}\)

\(\left(x-3\right):\left[\frac{1}{2}.\left(-1\frac{3}{4}\right)\right]=-2\frac{1}{2}\)

  \(\left(x-3\right):\left(\frac{1}{2}.\frac{-7}{4}\right)=\frac{-5}{2}\)

     \(\left(x-3\right):\frac{-7}{8}=\frac{-5}{2}\)

       \(x-3=\frac{-5}{2}.\frac{-7}{8}\)

        \(x-3=\frac{35}{16}\)

                  \(x=\frac{35}{16}+3\)

                  \(x=\frac{35+48}{16}=\frac{83}{16}\)

\(\frac{27^5}{81^3}=\frac{\left(3^3\right)^5}{\left(3^4\right)^3}=\frac{3^{15}}{3^{12}}=3^3=27\)

_Minh ngụy_

Ta có :27⁵ : 81³

 = (3³)⁵ : (3⁴)³ 

= 3^3.5 : 3^4.3 

= 3¹⁵ : 3¹² 

= 3^{15 - 12}

= 3³

= 27

Chúc bạn học tốt !!!!!

2.(x + 3) = 2³ . 3²

=> 2.(x + 3) = 8.9

=> 2.(x + 3) = 72

=>     x + 3  = 72 : 2

=>     x + 3  = 36

=>     x        = 36 - 3

=>     x        = 33

Chúc bạn học tốt !!!!!

\(2x+3=2^3+3^2\)

\(\Leftrightarrow2x+3=8+9\)

\(\Leftrightarrow2x+3=17\)

\(\Leftrightarrow2x=17-3\)

\(\Leftrightarrow2x=14\)

\(\Leftrightarrow x=7\)

_Hắc phong_

3k=(...01)

do 3*0=0 nen k phai thuoc n*

a) 2^x = 64

=> 2^x = 2⁶

=>    x = 6

b) 5^x = 7^x

=> 7^x - 5^x = 0

=> 5^x(2^x - 1) = 0

=> \(\orbr{\begin{cases}5^x=0\\2^x-1=0\end{cases}}\)\(\Rightarrow\orbr{\begin{cases}x\in\varnothing\\2^x=1\end{cases}}\)\(\Rightarrow2^x=2^0\Rightarrow x=0\)

c) 5^x . 5³ = 125

=>  5^{x + 3} = 5³

=>    x + 3 = 3

=>    x       = 0

d) 3^x - 17 = 64

=> 3^x        = 64 + 17

=> 3^x        = 81

=> 3^x        = 3⁴

=>   x        = 4

e) (3x - 5)³ = 5² . 2⁴ + 600

=> (3x - 5)³ = 25.16 + 600

=>  (3x - 5)³ = 400+ 600

=>  (3x - 5)³ = 1000

=>  (3x - 5)³  = 10³

=>   3x - 5     = 10

=>   3x          = 15

=>     x          = 15 : 3

=>     x           = 5

g) (5x - 15)³ = (5x - 15)⁷

=> (5x - 15)⁷ - (5x - 15)³ = 0

=> (5^x - 15)³. [(5x - 15)⁴ - 1] = 0

=> \(\orbr{\begin{cases}\left(5x-15\right)^3=0\\\left(5x-15\right)^4-1=0\end{cases}\Rightarrow\orbr{\begin{cases}\left(5x-15\right)=0\\\left(5x-15\right)^4=1\end{cases}\Rightarrow}\orbr{\begin{cases}5x-15=0\\5x-15=\pm1\end{cases}}}\)

Nếu 5x - 15 =0

=> 5x = 15

=>   x = 3

Nếu 5x - 15 = 1

=> 5x = 16

=>   x = 16 : 5

=>   x = 16/5

Nếu 5x - 16 = -1

=> 5x = 14

=>   x = 14 : 5

=>   x = 14/5

Vậy \(x\in\left\{3;\frac{16}{5};\frac{14}{5}\right\}\)

a) 2^x = 64

Vì 2⁶ = 64 nên x = 6

Vậy x = 6

b) 5^x = 7^x

Vì 5⁰ = 1 và 7⁰ = 1 

=> x = 0

Vậy, x = 0

c) 5^x . 5³ = 625

Ta có 625 = 5⁴

 nên 5^x . 5³ = 5⁴

5^x+3 = 5⁴

=> x = 1

Vậy x = 1

d) 3^x - 17 = 64

3^x = 64 + 17 = 81 = 3⁴

=> x = 4

Vậy x = 4

e) ( 3x - 5 ) ³ = 5² . 2⁴ + 600

( 3x - 5 ) ³ = 25 . 16 + 600 = 1000 = 10³

=> 3x - 5 = 10

3x = 10 + 5 = 15

x = 15 : 3 = 5

Vậy x = 5

g) ( 5x - 15 ) ³ = ( 5x - 15 ) ⁷

=> (5x - 15 ) ³ : ( 5x - 15 ) ⁷ = 1

( 5x - 15 ) ^{3 - 7} = 1

( 5x - 15 ) ^-4 = 1 = 1^-4 = -1^-4

=> 5x - 15 = 1 hoặc 5x - 15 = -1

5x = 1 + 15 hoặc 5x = -1 + 15

5x = 16 hoặc 5x = 14

\(x=\frac{16}{5}\) hoặc \(x=\frac{14}{5}\)

Vậy, \(x\in\left\{\frac{16}{5};\frac{14}{5}\right\}\)

Cbht

125⁶ và 25⁸

125⁶=125.125.125.125.125.125=5³.5³.5³.5³.5³.5³=5^3+3+3+3+3+3=5¹⁸

25⁸=25.25...25(8 chữ số 25)=5².5²...5²(8 chữ số 5²)=5^{2+2+2+2+2+2+2+2}=5¹⁶

Vì 5¹⁸>5¹⁶

=> 125⁶>25⁸

350² và 2⁷⁵

350²=350.350=2.5².7.2.5².7=2².5⁴.7²

2⁷⁵=2.2.2....2(75 chữ số 2)=2⁴.2¹⁰.2⁶..2⁵⁰

Vì 2².5⁴.7²<2⁴.2¹⁰.2⁶(2²<2⁴;5⁴<2¹⁰;7²<2⁶)

=>350²<2⁷⁵

Chúc bạn học tốt!

\(210+\left(y-15\right)\times3=195\)

\(210+\left(y-15\right)=195:3=65\)

\(y-15=210-65=145\)

\(\Rightarrow x=145+15=160\)

Vậy \(x=160\)

210 + (y - 15) x 3 = 195

          (y - 15) x 3  = 195 - 210

          (y - 15) x 3  = - 15

            y - 15        = -15 : 3

            y - 15        = - 5

            y               = -5 + 15

            y               = 10

120 - 4x(y - 3) = 136

=> 4x(y - 3)     = 136 - 120

=> 4x(y - 3)     = 16

=>   x(y - 3)     = 16 : 4

=>   x(y - 3)     = 4

Mà 4 = 1.4 = 2.2 = (-1).(-4) = (-2).(-2)

Lập bảng xét tất cả 6 trường hợp : 

Vậy các cặp (x,y) thỏa mãn là : (1;7) ; (2;5) ; (4;4) ; (-2 ; 1) ; (-1 ; -1) ; (- 4;2)

120 - 4(y - 3) = 136

<=> -4(y - 3) = 136 - 120

<=> -4(y - 3) = 16

<=> y - 3 = 16 : (-4)

<=> y - 3 = -4

<=> y = -4 + 3

<=> y = -1

=> y = -1

a) \(2^3\cdot4^5=2^3\cdot2^{10}=2^{13}\)

b) \(3^4\cdot27^2=3^4\cdot3^6=3^{10}\)

c) \(16^{10}:8^2=2^{40}:2^6=2^{34}\)

d) \(12^3:3^3=\left(12:3\right)^3=4^3\)

e) \(3^4\cdot2^4=\left(3\cdot2\right)^4=6^4\)

g) \(9^{13}\cdot5^{26}=9^{13}\cdot25^{13}=\left(9\cdot25\right)^{13}=225^{13}\)

=))

\(A=124\left(\frac{1}{1.1985}+\frac{1}{2.1986}+\frac{1}{3.1987}+...+\frac{1}{16.2000}\right)\)

      \(=\frac{124}{1984}.\left(1-\frac{1}{1985}+\frac{1}{2}-\frac{1}{1986}+...+\frac{1}{16}-\frac{1}{2000}\right)\)

       \(=\frac{1}{16}\left[\left(1+\frac{1}{2}+...+\frac{1}{16}\right)-\left(\frac{1}{1985}+\frac{1}{1986}+...+\frac{1}{2000}\right)\right]\)

  Và \(B=\frac{1}{1.17}+\frac{1}{2.18}+...+\frac{1}{1984.2000}\)

             \(=\frac{1}{16}\left[\left(1-\frac{1}{17}+\frac{1}{2}-\frac{1}{18}+...+\frac{1}{1984}-\frac{1}{2000}\right)\right]\)

              \(=\frac{1}{16}\left[\left(1+\frac{1}{2}+...+\frac{1}{1984}\right)-\left(\frac{1}{17}+\frac{1}{18}+...+\frac{1}{2000}\right)\right]\)

=      \(\frac{1}{16}\)  .    \(\left[\left(1+...+\frac{1}{16}\right)+\left(\frac{1}{17}+...+\frac{1}{1984}-\frac{1}{17}-...-\frac{1}{1984}\right)-\left(\frac{1}{1985}+...+\frac{1}{2000}\right)\right]\)

 = \(=\frac{1}{16}\left[\left(1+\frac{1}{2}+...+\frac{1}{16}\right)-\left(\frac{1}{1985}+\frac{1}{1986}+...+\frac{1}{2000}\right)\right]\)

Vậy A = B