If $\log{a} = p$, $\log{c} = 2p$ and $\log{e} = 3p$, then what is $(ace)^\frac{1}{p}$ equal to?

What is the number of solutions of $\log_4(x - 1) = \log_2(x - 3)$?

For $x \geq y > 1$, let $\log_x\left( \frac{x}{y} \right) + \log_y\left(\frac{y}{x}\right) = k$, then the value of $k$ can never be equal to :