MCQ
Let $a , b , c$ be three distinct positive real numbers such that $(2 a)^{\log _{\varepsilon} a}=(b c)^{\log _e b}$ and $b^{\log _e 2}=a^{\log _e c}$. Then $6 a+5 b c$ is equal to $........$.
- A$6$
- B$4$
- C$3$
- ✓$8$
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upto $\infty=2\left(\sqrt{\frac{b}{a}}+1\right) \log _e\left(\frac{a}{b}\right)$, where $a$ and $b$ are integers with $\operatorname{gcd}(a, b)=1$, then $11 a+18 b$ is equal to ...............