Question

[Trương Quỳnh Gia Kim]

Tìm x ϵ N 

\(4^{15}.9^{15}\le2^x.3^x\le18^{16}.2^{16}\)

Answer 1

[Khanh Lê]

\(4^{15}\cdot9^{15}\le2^x\cdot3^x\le18^{16}\cdot2^{16}\)

\(\Rightarrow\left(2^2\right)^{15}\cdot\left(3^2\right)^{15}\le2^x\cdot3^x\le\left(2\cdot3^2\right)^{16}\cdot2^{16}\)

\(\Rightarrow2^{30}\cdot3^{30}\le2^x\cdot3^x\le2^{32}\cdot3^{32}\)

\(\Rightarrow x=31\)