Đáp án:

\[\begin{array}{l}
{\log _a}bc = 2 = > bc = {a^2}\\
{\log _b}ac = 4 = > ac = {b^4}\\
= > \left\{ \begin{array}{l}
{c^2}ab = {a^2}{b^4}\\
{b^5}c = {a^3}c
\end{array} \right.\\
= > \left\{ \begin{array}{l}
{c^2} = {b^3}a\\
{b^5} = {a^3}
\end{array} \right. = > {c^2} = \sqrt[5]{{{a^9}}}a = > c = \sqrt[5]{{{a^7}}}\\
= > ab = \sqrt[5]{{{a^3}}}a = \sqrt[5]{{{a^8}}} = > {\log _c}ab = 8/7
\end{array}\]