The value of $\log _4 18$ is

If $\log_{4}5 = a$ and $\log_{5}6 = b$,then $\log_{3}2$ is equal to

If $x_n > x_{n-1} > \dots > x_2 > x_1 > 1$,then the value of $\log_{x_1} \log_{x_2} \log_{x_3} \dots \log_{x_n} (x_n^{x_{n-1}^{\dots^{x_1}}})$ is:

The set of all real values of $x$ for which $f(x) = \log_2(2^x - 2) + \sqrt{1 - x}$ is real is:

If $x+\log _{10}\left(1+2^{x}\right)=x \log _{10} 5+\log _{10} 6$, then the value of $x$ is

The solution to the equation ${9^x} - {2^{x + 1/2}} = {2^{x + 3/2}} - {3^{2x - 1}}$ is: