If ${{\log x} \over {b - c}} = {{\log y} \over {c - a}} = {{\log z} \over {a - b}},$ then which of the following is true
$xyz = 1$
${x^a}{y^b}{z^c} = 1$
${x^{b + c}}{y^{c + a}}{z^{a + b}} = 1$
All of These
If $log_ab + log_bc + log_ca$ vanishes where $a, b$ and $c$ are positive reals different than unity then the value of $(log_ab)^3 + (log_bc)^3 + (log_ca)^3$ is
If ${\log _k}x.\,{\log _5}k = {\log _x}5,k \ne 1,k > 0,$ then $x$ is equal to
The value of ${\log _3}\,4{\log _4}\,5{\log _5}\,6{\log _6}\,7{\log _7}\,8{\log _8}\,9$ is
The number of solution of ${\log _2}(x + 5) = 6 - x$ is
If $\log x:\log y:\log z = (y - z)\,:\,(z - x):(x - y)$ then