so sánh luỹ thừa toán 8

Q

quynhphamdq

Ta có:
$2009^{2010}$=$2009^{2009}$.2009(1)
Vì $2010^{2009}$:$2009^{2009}$=$\dfrac{2010}{2009}^{2009}$
=>$2010^{2009}$=$2009^{2009}$.$\dfrac{2010}{2009}^{2009}$(2)
Vì $\dfrac{2010}{2009}$ sấp sỉ 1 như vậy $(\dfrac{2010}{2009})^{2009}$ sấp sỉ 3
=>$(\dfrac{2010}{2009})^{2009}$<2009
=>$2009^{2009}$.2009>$2009^{2009}$.$(\dfrac{2010}{2009})^{2009}$
hay $2009^{2010}$> $2010^{2009}$
 
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C

congchuaquynh44

tại sao vậy?

Vì $\dfrac{2010}{2009}$ sấp sỉ 1 như vậy $\dfrac{2010}{2009}^{2009}$ sấp sỉ 3
sao lại biết được xấp xỉ 3 ạ?
 
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