Question

Mn ơi, giúp em với. Em cảm ơn ạ!

Answer 1

\(4^{15}.9^{15}< 2^n.3^n< 18^{16}.2^{16}\)

⇒\(\left(4.9\right)^{15}< \left(2.3\right)^n< \left(18.2\right)^{16}\)

⇒\(\left(6^2\right)^{15}< 6^n< \left(6^2\right)^{16}\)

⇒\(6^{30}< 6^n< 6^{32}\)

⇒\(6^n=6^{31}\)

⇒n=31

Answer 2

\(4^{15}\cdot9^{15}< 2^n\cdot3^n< 18^{16}\cdot2^{16}\\ \Leftrightarrow\left(4\cdot9\right)^{15}< \left(2\cdot3\right)^n< \left(18\cdot2\right)^{16}\\ \Leftrightarrow36^{15}< 6^n< 36^{16}\\ \Leftrightarrow6^{30}< 6^n< 6^{32}\\ \Leftrightarrow n=31\)