Oblicz a) [latex]log _{3} frac{1}{27} [/latex] b) [latex]log _{ frac{1}{27} } 3[/latex] c) [latex]log _{ sqrt{3} } 27[/latex] d) [latex]log _{27} 3 sqrt{3} [/latex] Proszę o dokładne obliczenia. Dziękuję.

[latex]a) log_3frac{1}{27}=log_327^{-1}=log_3(3^3)^{-1}=log_33^{-3}=-3log_33=-3\\\b) log_frac{1}{27}3=log_frac{1}{27}(3^3)^{frac{1}{3}}=frac{1}{3}log_frac{1}{27}27=frac{1}{3}log_frac{1}{27}(frac{1}{27})^{-1}\\=-frac{1}{3}log_frac{1}{27}frac{1}{27}=-frac{1}{3}[/latex] [latex]c) log_{sqrt3} 27=log_{sqrt3}3^3=3log_{sqrt3}3=3log_{sqrt3}(sqrt3)^2\\=2cdot3log_{sqrt3}sqrt3=6\\\d) log_{27}3sqrt3=log_{27}sqrt{3^2cdot3}=log_{27}sqrt{3^3}=log_{27}sqrt{27}\\=log_{27}27^{frac{1}{2}}=frac{1}{2}log_{27}27=frac{1}{2}[/latex] ©DRK