[Lớp 12]pt mũ

H

hthtb22

$$5^x.\sqrt[x+1]{8^x}=100$$

$$\Leftrightarrow log_{5} 5^x.\sqrt[x+1]{8^x}=log_{5}100 $$


$$\Leftrightarrow x + 3\dfrac{x}{x+1} log_{5}2=2+2log_{5}2$$

$$\Leftrightarrow (x-2)(1+\dfrac{log_{5}2}{x+1})=0$$

Vậy $\boxed{x=2.} \blackquare$
 
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