Rozwiązanie:
[tex]log_{ab}a=4\\(ab)^{4}=a\\a^{4}b^{4}=a\\b^{4}=a^{-3}\\b=(a^{-3})^{\frac{1}{4} }=a^{-\frac{3}{4} }[/tex]
Zatem:
[tex]log_{ab}\frac{\sqrt[3]{a} }{\sqrt{b} } =log_{(a*a^{-\frac{3}{4} )}}\frac{a^{\frac{1}{3} }}{(a^{-\frac{3}{4} })^{\frac{1}{2} }}=log_{a^{\frac{1}{4}} }\frac{a^{\frac{1}{3} }}{a^{-\frac{3}{8} }} =4log_{a}a^{\frac{17}{24} }=4*\frac{17}{24} =\frac{17}{6} =2,8(3)[/tex]
