Basic of Mathematics question bank (Maths)

Let $a, b, c$ be the three distinct positive real numbers such that ${\left(2a\right)}^{{\log }_{e}a}={\left(bc\right)}^{{\log }_{e}b}$ and $b^{{\log }_{e}2}=a^{{\log }_{e}c}$ Then $6a+5bc$ is equal to ______.

Let $S=\left\{x\in \left[-6,3\right]-\left\{-2,2\right\}:\frac{\left|x+3\right|-1}{\left|x\right|-2}\ge 0\right\}$ and $T=\left\{x\in Z:x^2-7\left|x\right|+9\le 0\right\}$. Then the number of elements in $S\cap T$ is