[tex]ab>0\wedge ab\neq 1 \\\log_{ab}{a}=4\\(ab)^4=a\\b=a^{-3/4}\\\log_{ab}{\frac{\sqrt[3]a}{\sqrt b}}=\log_{ab}{\sqrt[3]a}-\log_{ab}{\sqrt{b}}=\\\frac{1}{3}\log_{ab}{a}-\frac{1}{2}\log_{ab}{b}=\frac{4}{3}-\frac{1}{2}\cdot\left(-\frac{3}{4}\right)\log_{ab}a=\frac{4}{3}+\frac{3}{2}=\frac{17}{6}[/tex]
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