Question

So sanh: \(3^{39}\) va \(11^{21}\)

Answer 1

\(3^{39}and11^{21}\)

\(3^{39}< 3^{42};3^{42}=3^{6.7}=\left(3^6\right)^7=729^7\)

\(11^{21}=11^{3.7}=\left(11^3\right)^7=1331^7\)

Mà \(729^7< 1331^7\)

\(\Rightarrow3^{42}< 11^{21}\)

Answer 2

Giải:

Ta có:

\(3^{39}=\left(3^{13}\right)^3=1594323^3\)

\(11^{21}=\left(11^7\right)^3=19487171^3\)

Vì \(1594323< 19487171\)

Nên \(1594323^3< 19487171^3\)

Hay \(3^{39}< 11^{21}\)

Vậy \(3^{39}< 11^{21}\).