oblicz wartośćwyrażenia: log pierwiastek z 128 + log 32 do potęgi 1/3 ___________________________ log(2 pierwiastek z 2)

[latex]logsqrt{128}=logsqrt{2^7}=log2^frac{7}{2}=frac{7}{2}log2\ log32^{frac{1}{3}}=log(2^5)^frac{1}{3}}=log2^frac{5}{3}=frac{5}{3}log2\ log2sqrt{2}=log2^frac{3}{2}=frac{3}{2}log2[/latex]   [latex]frac{frac{7}{2}log2+frac{5}{3}log2}{frac{3}{2}log2}=frac{frac{21}{6}log2+frac{10}{6}log2}{frac{3}{2}log2}=frac{frac{31}{6}log2}{frac{3}{2}log2}=frac{frac{31}{6}}{frac{3}{2}}=frac{31}{6}cdot frac{2}{3}=frac{31}{9}[/latex]