Rewrite the equation using exponent rules.

We know that $2^{2x} = (2^x)^2$.
So the equation becomes:

$$(2^x)^2 - 18 \times 2^x = 40$$

Let $y = 2^x$. Substitute $y$ into the equation:

$$y^2 - 18y = 40$$

$$y^2 - 18y - 40 = 0$$

Factor the quadratic equation:

$$(y - 20)(y + 2) = 0$$

This gives two possible values for $y$:

$$y - 20 = 0 \implies y = 20$$ $$y + 2 = 0 \implies y = -2$$

Case 1: $y = 20$

$$2^x = 20$$

Take the logarithm of both sides (e.g., base 10 or natural log):

$$\log(2^x) = \log(20)$$ $$x \log(2) = \log(20)$$ $$x = \frac{\log(20)}{\log(2)}$$

Using a calculator:

$$x \approx \frac{1.30103}{0.30103} \approx 4.3219$$

Case 2: $y = -2$

$$2^x = -2$$

An exponential function with a positive base, like $2^x$, is always positive for real values of $x$. Therefore, there is no real solution for $x$ in this case.

The only real solution for $x$ is:

$$\boxed{x = \frac{\log(20)}{\log(2)} \approx 4.3219}$$

7. Given that $\text{Sin}(x - 30)^0 - \text{Cos}(4x)^0 = 0$. Find the $\text{tan}(2x+30)^0$

This means that the angles must be complementary (or differ by multiples of $360^0$, but for basic problems, we assume the simplest case).
So, we can equate the angles:

$$(x - 30)^0 + (4x)^0 = 90^0$$

$$x - 30 + 4x = 90$$ $$5x - 30 = 90$$ $$5x = 90 + 30$$ $$5x = 120$$ $$x = \frac{120}{5}$$ $$x = 24$$

First, calculate the angle:

$$2x + 30 = 2(24) + 30$$ $$2x + 30 = 48 + 30$$ $$2x + 30 = 78$$

Now, find the tangent of this angle:

$$\text{tan}(78)^0$$

Using a calculator:

$$\text{tan}(78)^0 \approx 4.7046$$

The value is:

$$\boxed{\text{tan}(2x+30)^0 \approx 4.7046}$$