2. Determine all real solutions of the equation

$$
2^{x}+3^{x}-4^{x}+6^{x}-9^{x}=1
$$
Solution. Let $2^{x}=a$ and $3^{x}=b$. The equation transforms into

$$
1+a^{2}+b^{2}-a-b-a b=0
$$

which is equivalent to the equation

$$
(1-a)^{2}+(a-b)^{2}+(b-1)^{2}=0
$$

From the last equation, it follows that $a=b=1$, from which we get that $x=0$.