Question

So sánh các cặp số sau:

A) 2^90 và 5^36

B) 2^27 và 3^18

Answer 1

\(\left\{{}\begin{matrix}2^{90}=\left(2^{10}\right)^9=1024^9\\5^{36}=\left(5^4\right)^9=625^9\end{matrix}\right.\)

\(1024^9>625^9\Leftrightarrow2^{90}>5^{36}\)

\(\left\{{}\begin{matrix}2^{27}=\left(2^3\right)^9=8^9\\3^{18}=\left(3^2\right)^9=9^9\end{matrix}\right.\)

\(8^9< 9^9\Leftrightarrow2^{27}< 3^{18}\)

Answer 2

Giải:

a) \(\left\{{}\begin{matrix}2^{90}=\left(2^5\right)^{18}=32^{18}\\5^{36}=\left(5^2\right)^{18}=25^{18}\end{matrix}\right.\)

Vì \(32>25\)

\(\Leftrightarrow32^{18}>25^{18}\)

Hay \(2^{90}>5^{36}\)

Vậy \(2^{90}>5^{36}\).

b) \(\left\{{}\begin{matrix}2^{27}=\left(2^3\right)^9=8^9\\3^{18}=\left(3^2\right)^9=9^9\end{matrix}\right.\)

Vì \(8< 9\)

\(\Rightarrow8^9< 9^9\)

Hay \(2^{27}< 3^{18}\)

Vậy \(2^{27}< 3^{18}\).

Chúc bạn học tốt!