`a, 2^(x-3) = 2^5`

`x - 3 = 5`

`x= 8`

`, 5^(x+1) = 5^3`

`x + 1 =3`

`x = 2`

`4^(2x+1) = 6`

`2x + 1 = 1,3`

`x = 0,15`

a, 2^x-3 = 32

    2^{x -3} = 2⁵

   x  - 3 = 5

  x = 5 + 3

  x = 8

b, 5^{x + 1} = 125

    5^{x + 1} = 5³

      x + 1 = 3

     x = 3 -1

     x = 2

c, 4^2x + 1 = 6

    16^x = 5

     x = log₁₆5

\(81.9^5.3^{2.x}=3^{11}\\ \Leftrightarrow3^4.\left(3^2\right)^5.3^{2.x}=3^{11}\\ \Leftrightarrow3^{4+2.5+2.x}=3^{11}\\ \Leftrightarrow4+2.5+2.x=11\\ \Leftrightarrow x=-\dfrac{3}{2}\)

`\dfrac{1}{81}.9^5 .3^{2x}=3^{11}`

`\dfrac{1}{9^2}.9^5 .3^{2x}=3^{11}`

`9^3 .3^{2x}=3^{11}`

`(3^2)^3 .3^{2x}=3^{11}`

`3^{6}. 3^{2x}=3^{11}`

`3^{6+2x}=3^{11}`

`6+2x=11`

`2x=11-6=5`

`x=5/2`

30:60 nhé

chắc là tính cả 60

26.7-17.9+13.26-17.11

=26(7+13)-17(11+9)

=26.20-17.20

=20(26-7)

=20.9

=180

ko vì 11 ko chia hết cho 3 nhưng 121372 chia hết cho 3

số 3;6;9 ở hàng đơn vị thì sẽ có khả năng chia hết cho 3 nhưng 121372 hàng đơn vị là 2

chắc mik sai

`2^{3}.125-125:5^{2}`

`=8.125-125. 1/25`

`=125.(8-1/25)`

`=125.199/25`

`=995`

2^3.125-125:5²

=8.125-125:25

=1000-5

=995

`5^{3}:5^{2}+2^{2}.3`

`=5^{3-2}+4.3`

`=5+12`

`=17`

\(2^{300}=\left(2^3\right)^{100}=8^{100}\\ 3^{200}=\left(3^2\right)^{100}=9^{100}\\ Vì:8^{100}< 9^{100}\left(8< 9\right)\Rightarrow2^{300}< 3^{200}\)

\(2022.2024=\left(2023-1\right).\left(2023+1\right)=2023.2023-1.1=2023^2-1< 2023^2\\ \Rightarrow2022.2024< 2023^2\)

A = 1 + 2 + 2² + 2³ + ......2¹¹

A = (1+2) + 2²(1 +2)+.....+ 2¹⁰(1+2)

A = 3 + 2².3 +......+ 2¹⁰.3

A = 3.( 1+ 2² +....+2¹⁰)

 3⋮ 3 ⇔ 3.(1+2²+.....+2¹⁰)⋮ 3⇔ A ⋮ 3 (đpcm)

\(A=1+2+2^2+...+2^{11}\\ =2^0+2^1+2^2+2^3+...+2^{10}+2^{11}\\ =2^0.\left(1+2\right)+2^2.\left(1+2\right)+...+2^{10}.\left(1+2\right)\\ =3.\left(2^0+2^2+2^4+2^6+2^8+2^{10}\right)⋮3\)