2.12: Exponential equations by substitution

The graph of the curve $y = p(4^{2x}) - q(4^{x})$ passes through the points $(0, 2)$ and $(0.5, 14)$. Find the value of $p$ and of $q$.

The variables $x$ and $y$ are connected by the equation $y = 10^{2x} - 2(10^{x})$. Using the substitution $u = 10^{x}$, or otherwise, find the exact value of $x$ when $y = 24$.