Suppose that $\log_2[\log_3 (\log_4a)] = \log_3 [\log_4 (\log_2b)] = \log_4 [\log_2 (\log_3c)] = 0$ then the value of $a + b + c$ is

The set of real values of $x$ for which the inequality $\log _{27} 8 \leq \log _{3} x \lt 9^{\frac{1}{\log _{2} 3}}$ holds is

The value of $(0.04^{log_{\sqrt{5}}(\frac{1}{4} + \frac{1}{8} + \frac{1}{16} + ...)})$ is __________.

If $x, y, z$ are positive real numbers such that $x^{12} = y^{16} = z^{24}$ and the three quantities $3 \log_y x, 4 \log_z y, n \log_x z$ are in arithmetic progression, then the value of $n$ is

If $\log_{18} 24 = p$, then $\log_{96} 108$ equals

If $\log_4 x = a$ and $\log_{25} x = b$, then $\log_x 10$ is

The value of $(\log_{3} 30)^{-1} + (\log_{4} 900)^{-1} + (\log_{5} 30)^{-1}$ is