$\text{Bài tập 1:}$

`{5^4. 20^4}/{25^5. 4^5}.`

`= {5^4. (5.4)^4}/{(5.5)^5. 4^5}.`

`= {5^4. 5^4 .4^4}/{5^5 .5^5. 4^5}.`

`= 1/{5.5. 4}.`

`=1/100.`

$\text{Bài tập 2:}$

`a)(5x-1).(2x-1/3)=0.`

$\text{⇒}$ \(\left[ \begin{array}{l}5x-1=0.\\2x-\dfrac{1}{3}=0.\end{array} \right.\) 

$\text{⇒}$ \(\left[ \begin{array}{l}5x=1.\\2x=\dfrac{1}{3}.\end{array} \right.\)

$\text{⇒}$ \(\left[ \begin{array}{l}x=\dfrac{1}{5}.\\x=\dfrac{1}{3}÷2.\end{array} \right.\)

$\text{⇒}$ \(\left[ \begin{array}{l}x=\dfrac{1}{5}.\\x=\dfrac{1}{3}.\dfrac{1}{2}.\end{array} \right.\)

$\text{⇒}$ \(\left[ \begin{array}{l}x=\dfrac{1}{5}.\\x=\dfrac{1}{6}.\end{array} \right.\)

$\text{Vậy x = $\dfrac{1}{5}$ hoặc x = $\dfrac{1}{6}$.}$

$\text{b) $2^{x-1}$ = 16.}$

$\text{⇒ $2^{x-1}$ = $2^{4}$.}$

$\text{⇒ x - 1 = 4.}$

$\text{⇒ x = 4 + 1.}$

$\text{⇒ x = 5.}$

$\text{Vậy x = 5.}$

$\text{c) $(x-1)^2$ = 25.}$

$\text{⇒ $(x-1)^2$ = $5^2$ = $(-5)^2$.}$

$\text{⇒}$ \(\left[ \begin{array}{l}x-1=5.\\x-1=-5.\end{array} \right.\)

$\text{⇒}$ \(\left[ \begin{array}{l}x=5+1.\\x=-5+1.\end{array} \right.\)

$\text{⇒}$ \(\left[ \begin{array}{l}x=6.\\x=-4.\end{array} \right.\)

$\text{Vậy x = 6 hoặc x = -4.}$

a) $\frac{5^{4}.20^{4}}{25^{5}.4^{5}}$  

=$\frac{(5.20)^{4}}{(25.4)^{5}}$  

=$\frac{100^{4}}{100^{5}}$  

=$\frac{1^{}}{100^{}}$  

Tìm x :

a)($5x-1^{}$) ($\frac{2x-1}{3}$) = $0^{}$ 

⇔\(\left[ \begin{array}{l}5x-1=0\\\frac{2x-1}{3} =0\end{array} \right.\)  

⇒\(\left[ \begin{array}{l}5x=1\\2x=1\end{array} \right.\) 

⇒\(\left[ \begin{array}{l}x=\frac{1}{5}\\x=\frac{1}{2}\end{array} \right.\) 

Vậy $x^{}$ ∈{$\frac{1}{5}$ ; $\frac{1}{2}$ }

b)$2^{x-1}$=16 

⇒$2^{x-1}$=$2^{4}$

⇒$x-1^{}$ =$4^{}$

⇒$x^{}$    =$5^{}$

c)$(x-1)^{2}$= $25^{}$ 

⇔$(x-1)^{2}$= $5^{2}$ =$(-5)^{2}$ 

⇒\(\left[ \begin{array}{l}x-1=5\\x-1=-5\end{array} \right.\) 

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

Vậy $x^{}$ ∈{$6^{}$ ;$-4^{}$ }

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