If ${\log _4}5 = a$ and ${\log _5}6 = b,$ then ${\log _3}2$ is equal to
${1 \over {2a + 1}}$
${1 \over {2b + 1}}$
$2ab + 1$
${1 \over {2ab - 1}}$
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 ${81^{(1/{{\log }_5}3)}} + {27^{{{\log }_{_9}}36}} + {3^{4/{{\log }_{_7}}9}}$ is equal to
The number of solution $(s)$ of the equation $log_7(2^x -1) + log_7(2^x -7) = 1$, is -
The sum of all the natural numbers for which $log_{(4-x)}(x^2 -14x + 45)$ is defined is -
The value of $\sqrt {(\log _{0.5}^24)} $ is