The value of ${81^{(1/{\log_5}3)}} + {27^{\log_9 36}} + {3^{4/{\log_7}9}}$ is

Let $p = 99$ and $q = 101$. Define $p_1 = \log_{10} \left(\frac{p+q}{2}\right)$ and $q_1 = \frac{1}{2}(\log_{10} p + \log_{10} q)$,and $p_2 = \log_{10} \left(\frac{p_1+q_1}{2}\right)$,$q_2 = \frac{1}{2}(\log_{10} p_1 + \log_{10} q_1)$. Then:

The value of $a^{\log_b x}$,where $a = 0.2$,$b = \sqrt{5}$,and $x = \frac{1}{4} + \frac{1}{8} + \frac{1}{16} + \dots$ to $\infty$ is:

The number of solution pairs $(x, y)$ of the simultaneous equations $\log _{1 / 3}(x+y)+\log _3(x-y)=2$ and $2^{y^2}=512^{x+1}$ is

The value of $x$ in the given equation $4^x - 3^{x - 1/2} = 3^{x + 1/2} - 2^{2x - 1}$ is

If $a^2 + 4b^2 = 12ab,$ then $\log(a + 2b)$ is