If $a = {\log _{24}}12,\,b = {\log _{36}}24$ and $c = {\log _{48}}36,$ then $1+abc$ is equal to
$2ab$
$2ac$
$2bc$
$0$
If ${1 \over 2} \le {\log _{0.1}}x \le 2$ then
If ${\log _k}x.\,{\log _5}k = {\log _x}5,k \ne 1,k > 0,$ then $x$ is equal to
If ${{\log x} \over {b - c}} = {{\log y} \over {c - a}} = {{\log z} \over {a - b}},$ then which of the following is true
Which is the correct order for a given number $\alpha $in increasing order
Let $\left(x_0, y_0\right)$ be the solution of the following equations $(2 x)^{\ln 2} =(3 y)^{\ln 3}$ $3^{\ln x} =2^{\ln y}$ . Then $x_0$ is