2. If $x>0$ applying the inequality of means we have

$4^{x} \cdot 9^{\frac{1}{x}}+9^{x} \cdot 4^{\frac{1}{x}}+6^{x+\frac{1}{x}} \geq 3 \sqrt[3]{4^{x} \cdot 9^{\frac{1}{x}} \cdot 9^{x} \cdot 4^{\frac{1}{x}} \cdot 6^{x+\frac{1}{x}}}=3 \cdot 6^{x+\frac{1}{x}} \geq 3 \cdot 6^{2}=108$

and equality holds if and only if $x=1$

$.5 p$
2. Solve in $\mathbb{R}$ the equation:

$$
4^{x} \cdot 9^{\frac{1}{x}}+9^{x} \cdot 4^{\frac{1}{x}}+6^{x+\frac{1}{x}}=108
$$