If ${\log _7}2 = m,$ then ${\log _{49}}28$ is equal to
$2\,(1 + 2m)$
${{1 + 2m} \over 2}$
${2 \over {1 + 2m}}$
$1 + m$
If $\log x:\log y:\log z = (y - z)\,:\,(z - x):(x - y)$ then
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
The value of ${\log _2}.{\log _3}....{\log _{100}}{100^{{{99}^{{{98}^{{.^{{.^{{{.2}^1}}}}}}}}}}}$ is
The number of solution $(s)$ of the equation $log_7(2^x -1) + log_7(2^x -7) = 1$, is -
The set of real values of $x$ for which ${2^{{{\log }_{\sqrt 2 }}(x - 1)}} > x + 5$ is