Question

So sánh

a)2⁹¹ và 5³⁵

b)2³³²và3²²³

Answer 1

a) Ta có: \(2^{91}>2^{90}=\left(2^5\right)^{18}=32^{18}\)

\(5^{35}< 5^{36}=\left(5^2\right)^{18}=25^{18}\)

Suy ra: \(2^{91}>32^{18}>25^{18}>5^{35}\)

Vậy \(2^{91}>5^{35}\)

b) Ta có: \(2^{332}< 2^{333}=\left(2^3\right)^{111}=8^{111}\left(1\right)\)

\(3^{223}>3^{222}=\left(3^2\right)^{111}=9^{111}\left(2\right)\)

Từ (1) và (2) suy ra \(2^{332}< 8^{111}< 9^{111}< 3^{223}\)

Vậy \(2^{332}< 3^{223}\)

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