Question

[pham van cuong]

so sanh 32^81 va 31^90

Answer 1

[ngonhuminh]

\(\left\{{}\begin{matrix}a=32^{81}\\b=31^{90}\end{matrix}\right.\)

\(\dfrac{a}{b}=\dfrac{2^{5.3^4}}{31^{2.3^2.5}}=\left(\dfrac{2^{3^2}}{31^2}\right)^{^{5.3^2}}\)

\(\dfrac{2^{10}}{2.31^2}< \dfrac{1024}{2.30^2}=\dfrac{1024}{1800}< 1\Rightarrow\dfrac{a}{b}< 1\Rightarrow a< b\)