Question

So sánh: \(2^{150}\)và \(^{3^{100}}\).Giải rõ ràng nhes

Answer 1

2¹⁵⁰=2^3.50= 8⁵⁰

3¹⁰⁰=3^2.50=9⁵⁰

Do 8⁵⁰ <  9⁵⁰ nên 2¹⁵⁰ < 3¹⁰⁰

Answer 2

\(2^{150}=2^{15\cdot10}=\left(2^{15}\right)^{10}=32768^{10}\)

\(3^{100}=3^{10\cdot10}=\left(3^{10}\right)^{10}=59049^{10}\)

Vì \(32768^{10}<59049^{10}\)

Nên \(2^{150}<3^{100}\)

Answer 3

Ta có: 

2^150 = (2^15)^10 = 32768^10

3^100 = (3^10)^10 = 59049^10

 Vì 59049^10 > 32768^10 nên 3^100 > 2^150