The sum of all the natural numbers for which $log_{(4-x)}(x^2 -14x + 45)$ is defined is -
$1$
$2$
$3$
$4$
If ${{\log x} \over {b - c}} = {{\log y} \over {c - a}} = {{\log z} \over {a - b}},$ then which of the following is true
The interval of $x$ in which the inequality ${5^{(1/4)(\log _5^2x)}}\, \geqslant \,5{x^{(1/5)(\log _5^x)}}$
$\log ab - \log |b| = $
$7\log \left( {{{16} \over {15}}} \right) + 5\log \left( {{{25} \over {24}}} \right) + 3\log \left( {{{81} \over {80}}} \right)$ is equal to
If ${a^x} = b,{b^y} = c,{c^z} = a,$ then value of $xyz$ is