1. Solve the equation:

$$
\left(2\left(2^{\sqrt{x}+3}\right)^{\frac{1}{2 \sqrt{x}}}\right)^{\frac{2}{\sqrt{x}-1}}=4
$$
1. Potentiation of a power $\left(2 \cdot 2^{\frac{\sqrt{x}+3}{2 \sqrt{x}}}\right)^{\frac{2}{\sqrt{x}-1}}=4$ ..... 0.5 points
Expressing the number 4 as a power ..... 0.5 points
Multiplication of powers $\left(2^{\frac{2 \sqrt{x}+\sqrt{x}+3}{2 \sqrt{x}}}\right)^{\frac{2}{\sqrt{x}-1}}=2^{2}$ ..... 0.5 points
Potentiation of powers $2^{\frac{(3 \sqrt{x}+3) \cdot 2}{2 \sqrt{x}}(\sqrt{x}-1)}=2^{2}$ ..... 0.5 points
Writing the equation $\frac{(3 \sqrt{x}+3) \cdot 2}{2 \sqrt{x}(\sqrt{x}-1)}=2$ ..... 0.5 points
Eliminating fractions $3 \sqrt{x}+3=2 \sqrt{x}(\sqrt{x}-1)$ ..... 0.5 points
Rearranging the equation $5 \sqrt{x}=2 x-3$ ..... 0.5 points
Squaring $25 x=4 x^{2}-12 x+9$ ..... 1 point
Rearranging the equation $4 x^{2}-37 x+9=0$ ..... 0.5 points
Both solutions $x_{1}=\frac{1}{4}$ and $x_{2}=9$ ..... 0.5 points
Verification and exclusion of the solution $\frac{1}{4}$ ..... 0.5 points