The solution of the equation ${\log _7}{\log _5}$ $(\sqrt {{x^2} + 5 + x} ) = 0$
$x = 2$
$x = 3$
$x = 4$
$x = - 2$
The set of real values of $x$ satisfying ${\log _{1/2}}({x^2} - 6x + 12) \ge - 2$ is
Let $\log _a b=4, \log _c d=2$, where $a, b, c, d$ are natural numbers. Given that $b-d=7$, the value of $c-a$ is
The number ${\log _{20}}3$ lies in
Let $a , b , c$ be three distinct positive real numbers such that $(2 a)^{\log _{\varepsilon} a}=(b c)^{\log _e b}$ and $b^{\log _e 2}=a^{\log _e c}$. Then $6 a+5 b c$ is equal to $........$.
$7\log \left( {{{16} \over {15}}} \right) + 5\log \left( {{{25} \over {24}}} \right) + 3\log \left( {{{81} \over {80}}} \right)$ is equal to