If ${a^x} = b$,${b^y} = c$,and ${c^z} = a$,then the value of $xyz$ is:

For a given number $\alpha > 1$,which of the following is the correct ascending order?

If $3^x = 4^{x-1}$,then $x = $

The sum of all the natural numbers for which $\log_{(4-x)}(x^2 - 14x + 45)$ is defined is -

The value of $6+\log_{\frac{3}{2}}\left(\frac{1}{3\sqrt{2}}\sqrt{4-\frac{1}{3\sqrt{2}}\sqrt{4-\frac{1}{3\sqrt{2}}\sqrt{4-\frac{1}{3\sqrt{2}}\dots}}}\right)$ is

The equation $x^{\frac{3}{4}(\log_2 x)^2 + \log_2 x - \frac{5}{4}} = \sqrt{2}$ has