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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Statement $-1$:An equation of a common tangent to these curve is $y = x + \sqrt 5 $
Statement $-2$: If the line, $y = mx + \frac{{\sqrt 5 }}{m}\left( {m \ne 0} \right)$ is their common tangent , then $m$ satisfies ${m^4} - 3{m^2} + 2 = 0$.