Đáp án:

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Bài `1`

`a,`

`(2x - 3)^2 = 25`

`↔` \(\left[ \begin{array}{l}(2x-3)^2=5^2\\(2x-3)^2=(-5)^2\end{array} \right.\) 

`↔` \(\left[ \begin{array}{l}2x-3=5\\2x-3=-5\end{array} \right.\) 

`↔` \(\left[ \begin{array}{l}2x=5 +3\\2x=-5+3\end{array} \right.\) 

`↔` \(\left[ \begin{array}{l}2x=8\\2x=-2\end{array} \right.\) 

`↔` \(\left[ \begin{array}{l}x=8÷2\\x=-2÷2\end{array} \right.\) 

`↔` \(\left[ \begin{array}{l}x=4\\x=-1\end{array} \right.\) 

Vậy `x=4` hoặc `x=-1`

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`b,`

`(2/5x - 1/3)^3 = (-1)/27`

`↔ (2/5x -1/3)^3 = (-1/3)^3`

`↔ 2/5x - 1/3 = (-1)/3`

`↔2/5x=(-1)/3 + 1/3`

`↔2/5x=0`

`↔x=0÷2/5`

`↔x=0`

Vậy `x=0`

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`c,`

`3^{x+2}=81`

`↔3^{x+2}=3^4`

`↔x+2=4`

`↔x=4-2`

`↔x=2`

Vậy `x=2`

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`d,`

`(x + 2012/2013)^6 = 0`

`↔ x  +2012/2013 = 0`

`↔ x = 0 - 2012/2013`

`↔ x = (-2012)/2013`

Vậy `x=(-2012)/2013`

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`e,`

`3^x + 3^{x+2}=810`

`↔ 3^x + 3^x × 3^2 = 810`

`↔ 3^x × (1 + 3^2) = 810`

`↔ 3^x × (1 + 9) = 810`

`↔ 3^x × 10 = 810`

`↔ 3^x = 810 ÷ 10`

`↔ 3^x=81`

`↔3^x=3^4`

`↔x=4`

Vậy `x=4`

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Bài `2`

`a,`

Có : `3^{222} = (3^2)^{111} = 9^{111}`

Có : `2^{333} = (2^3)^{111} = 8^{111}`

Ta thấy : `9 > 8`

`-> 9^{111} > 8^{111}`

`-> 3^{222} > 2^{333}`

Vậy `3^{222} > 2^{333}`

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`b,`

Có : `99^{20} = (99^2)^{10} = 9801^{10}`

Có : `9999^{10} = 9999^{10}`

Ta thấy : `9801 < 9999`

`-> 9801^{10} < 9999^{10}`

`-> 99^{20} < 9999^{10}`

Vậy `99^{20} < 9999^{10}`

a) $(2x-3)^2 = 25$

⇒ \(\left[ \begin{array}{l}x-3=5\\x-3=-5\end{array} \right.\) 

⇒\(\left[ \begin{array}{l}2x=5+3\\2x=-5+3\end{array} \right.\) 

⇒ \(\left[ \begin{array}{l}x=4\\x=-1\end{array} \right.\) 

$Vậy$ \(\left[ \begin{array}{l}x=4\\x=-1\end{array} \right.\) 

b) $($$\dfrac{2}{5}x$$-$ $\dfrac{1}{3})^3$ $=$ $-\dfrac{1}{27}$ 

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

⇒ $\dfrac{2}{5}x$ $= 0$

⇒ $x=0$

$Vậy$ $x=0$

c) $3^{x+2}=81$  

⇒ $3^x · 3² = 3^4$

⇒ $3^x=3^4:3^2$

⇒ $3^x$ $= 3^2$

⇒ $x=2$

$Vậy$ $x=2$

d) $(x+\dfrac{2012}{2013})^6$ $=0$

⇒ $x+\dfrac{2012}{2013}$ $=0$

⇒ $x= -\dfrac{2012}{2013}$

$Vậy$  $x= -\dfrac{2012}{2013}$

e) $3^x + 3^{x+2} = 810$ 

⇒ $3^x+3^x.3^2=810$ 

⇒ $3^x\left(1+3^2\right)=810$ ⇒ $3^x.10=810$

⇒ $3^x=81=3^4$ ⇒ $x=4$

$Vậy$ $x=4$

2 : So sánh

a)  $Vì$   $3^{222}$ $=$ $3^{111·2}$  $=$ $9^{111}$ 

          $2^{333}$ $=$ $2^{111·3}$  $=$ $8^{111}$

$Mà$ $9>8$

⇒ $3^{222}$ $>$ $2^{333}$

$Vậy$ $3^{222}$ $>$ $2^{333}$ 

b) $Vì$ $99^{20}$ = $99^{10·2}$  = $9801^{10}$ 

$Mà$ $9801<9999$ 

⇒ $99^{20}$ $<$ $9999^{10}$

$Vậy$ $99^{20}$ $<$ $9999^{10}$