Решите,пожалуйста,подробно логарифм

[latex]\displaystyle log^2_{ \sqrt{2}}(2 \sqrt{2})^{ \sqrt{32}}=(log_{ \sqrt{2}}( \sqrt{2}^3)^{ \sqrt{32}})^2 =(log_{ \sqrt{2}}( \sqrt{2})^{3 \sqrt{32}})^2= [/latex] [latex]\displaystyle =(3 \sqrt{32})^2=9*32= 288[/latex]