If ${{\log x} \over {b – c}} = {{\log y} \over {c – a}} = {{\log z} \over {a – b}},$ then which of the following is true

If $x = {\log _5}(1000)$ and $y = {\log _7}(2058)$ then

Solution set of equation

$\left| {1 – {{\log }_{\frac{1}{6}}}x} \right| + \left| {{{\log }_2}x} \right| + 2 = \left| {3 – {{\log }_{\frac{1}{6}}}x + {{\log }_{\frac{1}{2}}}x} \right|$ is $\left[ {\frac{a}{b},a} \right],a,b, \in N,$ then the value of $(a + b)$ is

Let $a=3 \sqrt{2}$ and $b=\frac{1}{5^{\frac{1}{6}} \sqrt{6}}$. If $x, y \in R$ are such that  $3 x+2 y=\log _a(18)^{\frac{5}{4}} \text { and }$  $2 x-y=\log _b(\sqrt{1080}),$  then $4 x+5 y$ is equal to. . . . 

If ${\log _7}2 = m,$ then ${\log _{49}}28$ is equal to