Exponential equations and inequalities

Find the solution of the equation $2^2\cdot 2^4\cdot 2^6\cdot \cdots \cdot 2^{2x}={\left(\frac{1}{32}\right)}^{-x-1}$.

For which values of parameter $m\in \mathbb{R}$ does the equation ${\left(\frac{1}{5}\right)}^x+m^2-9m+18=0$ have a solution?

The patient took a single dose of $50\mathrm{mg}$ of the drug. Within $3$ hours $40\mathrm{\%}$ of the dose was excreted from his body. The mass $m$ (mg) of the drug in the body after time $t$ (hours) is given by the formula $m(t)=m_0{a}^t$, where $m_0$ (mg) is the initial mass and $a$ is a constant. Calculate how much medicine the patient had in his body after $12$ hours.