The value of $\sqrt {(\log _{0.5}^24)} $ is
$-2$
$\sqrt {( - 4)} $
$2$
None of these
The number of solution pairs $(x, y)$ of the simultaneous equations $\log _{1 / 3}(x+y)+\log _3(x-y)=2$ $2^{y^2}=512^{x+1}$ is
The value of ${81^{(1/{{\log }_5}3)}} + {27^{{{\log }_{_9}}36}} + {3^{4/{{\log }_{_7}}9}}$ is equal to
The value of $\left(\left(\log _2 9\right)^2\right)^{\frac{1}{\log _2\left(\log _2 9\right)}} \times(\sqrt{7})^{\frac{1}{\log _4 7}}$ is. . . . . . .
Let $S$ be the sum of the digits of the number $15^2 \times 5^{18}$ in base $10$. Then,
The sum $\sum \limits_{n=1}^{\infty} \frac{2 n^2+3 n+4}{(2 n) !}$ is equal to :