If $x, y$ are real numbers such that $3^{(x/y)+1} - 3^{(x/y)-1} = 24$,then the value of $(x+y)/(x-y)$ is

If $a^2 + 4b^2 = 12ab,$ then $\log(a + 2b)$ 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 square root of $\frac{(0.75)^3}{1-0.75}+[0.75+(0.75)^2+1]$ is

Suppose $a, b, c$ are positive integers such that $2^a + 4^b + 8^c = 328$. Then,$\frac{a + 2b + 3c}{abc}$ is equal to

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