Let $\mathrm{a}, \mathrm{b}, \mathrm{c}$ be three distinct positive real numbers such that $(2 \mathrm{a})^{\log _{\mathrm{a}} \mathrm{a}}=(\mathrm{bc})^{\log _{\mathrm{a}} \mathrm{b}}$ and $\mathrm{b}^{\log _{\mathrm{a}} 2}=\mathrm{a}^{\log _{\mathrm{a}} \mathrm{c}}$. Then $6 a+5 b c$ is equal to $\_\_\_\_$ .1