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

If $x = \log_a(bc)$,$y = \log_b(ca)$,and $z = \log_c(ab)$,then which of the following is equal to $1$?

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

The set of real values of $x$ for which $\log_{0.2} \left( \frac{x + 2}{x} \right) \le 1$ is

If $a, b, c$ are distinct positive numbers,each different from $1$,such that $[(\log _b a)(\log _c a) - (\log _a a)] + [(\log _a b)(\log _c b) - (\log _b b)] + [(\log _a c)(\log _b c) - (\log _c c)] = 0$,then $abc =$

The number of solutions of $\log_{4}(x - 1) = \log_{2}(x - 3)$ is: