If ${x^{\frac{3}{4}(\log_3 x)^2 + \log_3 x - \frac{5}{4}}} = \sqrt{3}$,then $x$ has:

If ${x_n} > {x_{n - 1}} > ... > {x_2} > {x_1} > 1$,then the value of ${\log _{{x_1}}}{\log _{{x_2}}}{\log _{{x_3}}}.....{\log _{{x_n}}}({x_n}^{{x_{n - 1}}^{{.^{{.^{{.^{{x_1}}}}}}}}})$ is equal to

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

If $x = \log _2 \left( \sqrt {56 + \sqrt {56 + \sqrt {56 + \dots + \infty } } } \right)$,then:

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

If $a^x = b^y = c^z = d^w$, the value of $x\left(\frac{1}{y} + \frac{1}{z} + \frac{1}{w}\right)$ is