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 value of $6+\log _{\frac{3}{2}}\left(\frac{1}{3 \sqrt{2}} \sqrt{4-\frac{1}{3 \sqrt{2}} \sqrt{4-\frac{1}{3 \sqrt{2}} \sqrt{4-\frac{1}{3 \sqrt{2}} \ldots}}}\right)$ is
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 ${\log _{10}}3 = 0.477$, the number of digits in ${3^{40}}$ is
Let $x, y$ be real numbers such that $x>2 y>0$ and $2 \log (x-2 y)=\log x+\log y$ Then, the possible value(s) of $\frac{x}{y}$
If $x = {\log _b}a,\,\,y = {\log _c}b,\,\,\,z = {\log _a}c$, then $xyz$ is