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
For $y = {\log _a}x$ to be defined $'a'$ must be
The number of integral solutions $x$ of $\log _{\left(x+\frac{7}{2}\right)}\left(\frac{x-7}{2 x-3}\right)^2 \geq 0$ is
If $\log x:\log y:\log z = (y - z)\,:\,(z - x):(x - y)$ then
The interval of $x$ in which the inequality ${5^{(1/4)(\log _5^2x)}}\, \geqslant \,5{x^{(1/5)(\log _5^x)}}$
If $A = {\log _2}{\log _2}{\log _4}256 + 2{\log _{\sqrt 2 \,}}\,2,$ then $A$ is equal to