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 $
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 $........$.
If ${\log _{0.3}}(x - 1) < {\log _{0.09}}(x - 1)$ then $x \ne 1$ lies in
The number ${\log _2}7$ is
The number of solution $(s)$ of the equation $log_7(2^x -1) + log_7(2^x -7) = 1$, is -
The number of solution of ${\log _2}(x + 5) = 6 - x$ is