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

If $\log x : \log y : \log z = (y - z) : (z - x) : (x - y)$,then

The number of solutions of the equation $\frac{1}{2} \log _{\sqrt{3}}\left(\frac{x+1}{x+5}\right)+\log _{9}(x+5)^{2}=1$ is

If $x = \log_3 5$ and $y = \log_{17} 25$,then which of the following is correct?

If $a, b, c \neq 0$ and belong to the set $\{0, 1, 2, 3, \ldots, 9\}$, then $\log _{10}\left(\frac{a+10 b+10^2 c}{10^{-4} a+10^{-3} b+10^{-2} c}\right)$ is equal to

The value of $\log(\sin 1^{\circ}) \cdot \log(\sin 2^{\circ}) \cdot \log(\sin 3^{\circ}) \dots \log(\sin 179^{\circ})$ is: