If ${\log _7}2 = m,$ then ${\log _{49}}28$ is equal to
$2\,(1 + 2m)$
${{1 + 2m} \over 2}$
${2 \over {1 + 2m}}$
$1 + m$
If $x = {\log _5}(1000)$ and $y = {\log _7}(2058)$ then
If $a = {\log _{24}}12,\,b = {\log _{36}}24$ and $c = {\log _{48}}36,$ then $1+abc$ is equal to
Let $a, b, x$ be positive real numbers with $a \neq 1$, $x \neq 1$, ab $\neq 1$. Suppose $\log _{ a } b =10$, and $\frac{\log _{ a } x \log _{ x }\left(\frac{ b }{ a }\right)}{\log _{ x } b \log _{ ab } x }=\frac{ p }{ q }$, where $p$ and $q$ are positive integers which are coprime. Then $p+q$ is
If ${\log _5}a.{\log _a}x = 2,$then $x$ is equal to
If $a, b, c$ are distinct positive numbers, each different from $1$, such that $[{\log _b}a{\log _c}a - {\log _a}a] + [{\log _a}b{\log _c}b - {\log _b}b]$ $ + [{\log _a}c{\log _b}c - {\log _c}c] = 0,$ then $abc =$