Question

so sánh 2³⁶ và 3^27; 2²⁷ và 3¹⁸; 

Answer 1

\(2^{36}\)và \(3^{27}\)

\(2^{36}=2^{4.9}=\left(2^4\right)^9=16^9\)
\(3^{27}=3^{3.9}=\left(3^3\right)^9=27^9\)

Vì: \(16^9< 27^9\Rightarrow2^{36}< 3^{27}\)

\(2^{27}\)và \(3^{18}\)

\(2^{27}=2^{3.9}=\left(2^3\right)^9=8^9\)

\(3^{18}=3^{2.9}=\left(3^2\right)^9=9^9\)

Vì: \(8^9< 9^9\Rightarrow2^{27}< 3^{18}\)

Answer 2

Ta có:

2³⁶=(2⁴)⁹=16⁹

3²⁷=(3³)⁹=27⁹

Vì 16⁹ < 27⁹ nên 2³⁶ < 3²⁷

Ta có:

2²⁷=(2³)⁹=8⁹

3¹⁸=(3²)⁹=9⁹

Vì 8⁹ < 9⁹ nên 2²⁷ < 3¹⁸