If $x = {\log _a}(bc),y = {\log _b}(ca),z = {\log _c}(ab),$then which of the following is equal to $1$
$x + y + z$
${(1 + x)^{ - 1}} + {(1 + y)^{ - 1}} + {(1 + z)^{ - 1}}$
$xyz$
None of these
If ${a^2} + 4{b^2} = 12ab,$ then $\log (a + 2b)$ is
If ${\log _4}5 = a$ and ${\log _5}6 = b,$ then ${\log _3}2$ is equal to
${\log _4}18$ is
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 $........$.
If $x = {\log _5}(1000)$ and $y = {\log _7}(2058)$ then