Oblicz : log[latex] \ 7[/latex] 14 - log[latex] \ 7[/latex] 2 [latex] sqrt{7} [/latex]=  [latex] frac{27 ^{10} }{81^{5}* 9^{3} } [/latex]= log[latex] \ 6[/latex] 4[latex] sqrt{3} [/latex] + log[latex] \ 6[/latex] 9[latex] sqrt{2} [/latex]=

[latex]log_7 frac{14}{2 sqrt{7} } =log_7 frac{7}{ sqrt{7} } =log_7 frac{7^1}{7^{ frac{1}{2} } }=log_77^{ frac{1}{2} }= frac{1}{2} \ frac{(3^3)^{10}}{(3^4)^{5}*(3^2)^3} = frac{3^{30}}{3^{26}} =3^4\ log_6(4 sqrt{3} *9 sqrt{2} )=log_6(36 sqrt{6} )=log_6(6^2*6^{ frac{1}{2} })=log_66^{ frac{5}{2} }= frac{5}{2} [/latex]