Question

so sánh 101^15 và 9^29

Answer 1

Ta có : \(9^{29}< 9^{30}=9^{2.15}=\left(9^2\right)^{15}=81^{15}\)

Vì \(101^{15}>81^{15}\)

\(\Rightarrow101^{15}>9^{30}\)

\(\Rightarrow101^{15}>9^{29}\)

Vậy \(101^{15}>9^{29}\)

Answer 2

Answer 3

Ta có :

9²⁹ < 9³⁰

Mà 9³⁰ = (9²)¹⁵ = 81¹⁵ < 101¹⁵

⇒ 101¹⁵ > 9²⁹

Answer 4

\(101^{15}=101^{3^5}=303^5=101^5.3^5\)

\(9^{29}=3^{2^{29}}=3^{58}=3^{50}.3^5.3^3=3^{10^5}.3^5.3^3=59049^5.3^5.3^3\)

\(101^5< 59049^5\)

\(3^5=3^5\)

\(\Rightarrow101^{15}< 9^{29}\)