1. Tính 4^2.25^2.2^5.5^3/2^3.5^2 2. Tìm x biết a.(x-1)^3 =27, b.x^2+x=0, c.(2x+1)^2=25, d.(2x-3)^2=9=3^2, e.5^x+2=625, f.(x-1)^x+2= (x-1)^x+4, g. (2

Bài 1:

`(4².25².2^5. 5^3)/(2^3. 5^2)`
`=((2^2)^2.(5^2)^2. 2^5 .5^3)/(2^3 .5^2)`
`=(2^4 .5^4 .2^5 .5^3)/(2^3 .5^2)`
`=(2^9 .5^7)/(2^3 .5^2)`
`=2^6 .5^5`
`=64.3125`
`=200 000`

Bài 2:

`a)(x-1)³=27`

    `(x-1)³=3³`

    `x-1=3`

    `x=3+1`

    `x=4`

`b)x²+x=0`

`⇔x(x+1)=0`

`⇔`\(\left[ \begin{array}{l}x=0\\x+1=0\end{array} \right.\)
`⇔`\(\left[ \begin{array}{l}x=0\\x=-1\end{array} \right.\)

`c)(2x+1)²=25`

`⇔(2x+1)²=5²`

`⇔`\(\left[ \begin{array}{l}2x+1=5\\2x+1=-5\end{array} \right.\)

`⇔`\(\left[ \begin{array}{l}2x=4\\2x=-6\end{array} \right.\)

`⇔`\(\left[ \begin{array}{l}x=2\\2x=-3\end{array} \right.\)

`d)(2x-3)²=9`

`⇔(2x-3)²=3²`

`⇔`\(\left[ \begin{array}{l}2x-3=3\\2x-3=-3\end{array} \right.\)

`⇔`\(\left[ \begin{array}{l}2x=3+3\\2x=-3+3\end{array} \right.\)

`⇔`\(\left[ \begin{array}{l}2x=6\\2x=0\end{array} \right.\)

`⇔`\(\left[ \begin{array}{l}x=3\\x=0\end{array} \right.\)

`e)5^(x+2)=625`

    `5^(x+2)=5^4`

    `x+2=4`

    `x=4-2`

    `x=2`

`f)(x-1)^(x+2)=(x-1)^(x+4)`

   `x+2=x+4`

   `x-x=4-2`

   `0x=2(`ko có giá trị nào thỏa mãn `x)`

`g)(2x-1)³=-8`

    `(2x-1)³=(-2)³`

    `2x-1=-2`

    `2x=-2+1`

    `2x=-1`

       `x=-1/2`

`h)1/4 . 2/6 . 3/8 . 4/10 . 5/12 …30/62 . 31/64=2^x`     
`⇒(1.2.3.4.5…30.31)/(4.6.8.10.12…62.64)=2^x`
`⇒(1.2.3.4.5…30.31)/(2.2.2.3.2.4.2.5.2.6…2.31.2.32)=2^x`
`⇒(1.2.3.4.5…30.31)/[(2.2.2.2.2…2.2).(2.3.4.5.6…31.32)]=2^x`
`⇒(1.2.3.4.5…30.31)/[2^31.(2.3.4.5.6…31.32)]=2^x`

`⇒(1.2.3.4.5…30.31)/[2^31.(2.3.4.5.6…31).32]=2^x`
`⇒1/(2^31. 32)=2^x`
`⇒1/(2^31. 2^5)=2^x`
`⇒1/(2^36)=2^x`
`⇒2^x .2^36=1`

`⇒2^(x+36)=2^0`
`⇒x+36=0`
`⇒x=0-36`
`⇒x=-36`

 

Trả lời