Which is the correct order for a given number $\alpha $in increasing order
${\log _2}\alpha ,\,{\log _3}\alpha ,\,{\log _e}\alpha ,\,{\log _{10}}\alpha $
${\log _{10}}\alpha ,\,{\log _3}\alpha ,{\log _e}\alpha ,{\log _2}\alpha $
${\log _{10}}\alpha ,\,{\log _e}\alpha ,\,{\log _2}\alpha ,\,{\log _3}\alpha $
${\log _3}\alpha ,\,{\log _e}\alpha ,\,{\log _2}\alpha ,\,{\log _{10}}\alpha $
The solution of the equation ${\log _7}{\log _5}$ $(\sqrt {{x^2} + 5 + x} ) = 0$
If ${1 \over 2} \le {\log _{0.1}}x \le 2$ then
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 product of all positive real values of $x$ satisfying the equation $x^{\left(16\left(\log _5 x\right)^3-68 \log _5 x\right)}=5^{-16}$is. . . . .
If ${\log _{10}}2 = 0.30103,{\log _{10}}3 = 0.47712,$ the number of digits in ${3^{12}} \times {2^8} $ is