[latex]log_frac{4}{9} (1 - frac{sqrt{3}}{3}) + log_frac{4}{9} (1+ frac{sqrt{3}}{3}) =log_frac{4}{9} [(1 - frac{sqrt{3}}{3})(1+ frac{sqrt{3}}{3})]= \\ =log_frac{4}{9} [1^2 - (frac{sqrt{3}}{3})^2] =log_frac{4}{9} (1 - frac{3}{9})=log_frac{4}{9} (1 - frac{1}{3})=log_frac{4}{9} frac{2}{3}= \\ =log_frac{4}{9} sqrt{frac{4}{9}}=log_frac{4}{9} (frac{4}{9})^{frac{1}{2}}=frac{1}{2} cdot log_frac{4}{9} frac{4}{9} = frac{1}{2} cdot 1 = frac{1}{2}[/latex] -------------------- Wykorzystano własności i wzory: 1) [latex]log_a b + log_a c = log_a (b cdot c)[/latex] 2) [latex](a - b)(a+ b) = a^2 - b^2[/latex] 3) [latex]sqrt{frac{4}{9}} = frac{2}{3}[/latex] 4) [latex]sqrt{frac{4}{9}}=(frac{4}{9})^{frac{1}{2}[/latex] 5) [latex]log_a b^n = n cdot log_a b[/latex] 6) [latex]log_a a = 1[/latex]
