\(\dfrac{x}{9}=\dfrac{3}{y}+\dfrac{1}{18}\left(y\ne0\right)\)

\(\Rightarrow\dfrac{2xy}{18y}=\dfrac{54}{18y}+\dfrac{y}{18y}\)

\(\Rightarrow2xy=54+y\)

\(\Rightarrow2xy-y=54\)

\(\Rightarrow xy-\dfrac{y}{2}=27\)

\(\Rightarrow y\left(x-\dfrac{1}{2}\right)=27\)

\(\Rightarrow\left(x-\dfrac{1}{2}\right);y\in\left\{1;3;9;27\right\}\)

\(\Rightarrow\left(x;\right)y\in\left\{\left(\dfrac{1}{2};27\right);\left(\dfrac{5}{2};9\right);\left(\dfrac{17}{2};3\right);\left(\dfrac{53}{2};1\right)\right\}\)

\(\Rightarrow\left(x;y\right)\in\varnothing\left(x;y\inℕ\right)\)

\(3^{8x+4}=81^{x+3}\)

\(3^{8x+4}=\left(3^4\right)^{x+3}\)

\(3^{8x+4}=3^{4x+12}\)

\(\Rightarrow8x+4=4x+12\)

\(\Rightarrow8x-4x=12-4\)

\(\Rightarrow4x=8\Rightarrow x=2\)

  3^{8.x + 4} = 81^{x + 3}

  3^{8.x + 4} = (3⁴)^{x + 3}

  3^{8.x + 4} = 3^{4.x + 12}

  8.x + 4 = 4.x + 12

8.x - 4.x = 12 - 4

        4.x = 8

           x = 8 : 4

           x = 2

\(2^x=2+2+2^2+...+2^{30}\)

\(\Rightarrow2^x=1+\left(1+2+2^2+...+2^{30}\right)\)

\(\Rightarrow2^x=1+\dfrac{2^{30+1}-1}{2-1}\)

\(\Rightarrow2^x=1+2^{31}-1\)

\(\Rightarrow2^x=2^{31}\)

\(\Rightarrow x=31\)

  2^x + 2^{x + 1} = 96

  2^x + 2^x . 2 = 96

 2^x . (1 + 2) = 96

         2^x . 3 = 96

              2^x = 96 : 3

              2^x = 32

              2^x = 2⁵

                x = 5

đáp số a rr

b

`#040911`

\(2^{10}\div8^5\\ =2^{10} \div\left(2^3\right)^5\\=2^{10}\div2^{15}=2^{-5} \)

Đề có nhầm gì k bạn?

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\(920+3^2.\left(2^2.5^3-6.5^2\right)\\ \\ \\ =920+9.\left(4.125-6.25\right)\\ \\ \\ =920+9.\left(500-150\right)\\ \\ \\ =920+9.350=920+3150=4070\)

   920 + 3² . (2² . 5³ - 6 . 5²)

= 920 + 9 . (4 . 125 - 6 . 25)

= 920 + 9 . (500 - 150)

= 920 + 9 . 350

= 920 + 3150

= 4070