$\log (\cosh 3 + \sinh 3) + \log (\cosh 3 - \sinh 3) = $

If $n = (2020)!$,then the value of $\frac{1}{\log _{2} n} + \frac{1}{\log _{3} n} + \frac{1}{\log _{4} n} + \ldots + \frac{1}{\log _{2020} n}$ is equal to:

$7\log \left( \frac{16}{15} \right) + 5\log \left( \frac{25}{24} \right) + 3\log \left( \frac{81}{80} \right) =$

The sum of the roots of the equation $x+1-2 \log _{2}\left(3+2^{x}\right)+2 \log _{4}\left(10-2^{-x}\right)=0$ is:

If $\log _{(3x-1)}(x-2) = \log _{(9x^2-6x+1)}(2x^2-10x-2)$,then $x$ equals

If ${\log _{12}}27 = a,$ then ${\log _6}16 = $