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

If $\log_{a}b + \log_{b}c + \log_{c}a = 0$,where $a, b,$ and $c$ are positive real numbers different from $1$,then the value of $(\log_{a}b)^3 + (\log_{b}c)^3 + (\log_{c}a)^3$ is

For $y = \log_a x$ to be defined,$a$ must be:

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

Which one of the following observations is correct for the features of the logarithm function to any base $b > 1$?

If $\log 2=a, \log 3=b, \log 7=c$ and $6^x=7^{x+4}$, then $x$ is equal to: