Log по основанию sqrt2 (log 2 3 *log 3 4 )

[latex]log_{\sqrt{2}} (log_2 3*log_3 4)=[/latex] [latex]log_a b*log_b c=log_a c[/latex] [latex]log_{\sqrt{2}} log_2 4=[/latex] [latex]log(\sqrt{2}} log_2 2^2[/latex] [latex]log_a b^n=n*log_a b[/latex] [latex]log_\sqrt{2}} (2*log_2 2)=[/latex] [latex]log_a a=1[/latex] [latex]=log_{\sqrt{2}} (2*1)=[/latex] [latex]log_{\sqrt{2}} 2=[/latex] [latex]log_{\sqrt{2}} (\sqrt{2})^2[/latex] [latex]2*log_{\sqrt{2}} \sqrt{2}=[/latex] [latex]2*1=[/latex] [latex]2[/latex] отвте: 2