CAT 2024 Slot 2 QA · Question 9

If $a,b$ and $c$ are positive real numbers such that $a>10\ge b\ge c$ and $\frac{{\log }_8(a+b)}{{\log }_{2}c}+\frac{{\log }_{27}(a-b)}{{\log }_{3}c}=\frac{2}{3}$, then the greatest possible integer value of $a$ is<