If $3^x=4^{x-1}$, then $x=$

$(A)$ $\frac{2 \log _3 2}{2 \log _3 2-1}$ $(B)$ $\frac{2}{2-\log _2 3}$ $(C)$ $\frac{1}{1-\log _4 3}$ $(D)$ $\frac{2 \log _2 3}{2 \log _2 3-1}$

The set of real values of $x$ for which ${2^{{{\log }_{\sqrt 2 }}(x - 1)}} > x + 5$ is

If $\log x:\log y:\log z = (y - z)\,:\,(z - x):(x - y)$ then

If $x = {\log _3}5,\,\,\,y = {\log _{17}}25,$ which one of the following is correct

The number of solution $(s)$ of the equation $log_7(2^x -1) + log_7(2^x -7) = 1$, is -

$7\log \left( {{{16} \over {15}}} \right) + 5\log \left( {{{25} \over {24}}} \right) + 3\log \left( {{{81} \over {80}}} \right)$ is equal to