Solve the equation (20)/((sqrt(2))^x) = (5)/(4) for x.

We have the equation:

$$\frac{20}{(\sqrt{2})^x} = \frac{5}{4}$$

Multiply both sides by $4(\sqrt{2})^x$:

$$20 \times 4 = 5 \times (\sqrt{2})^x$$ $$80 = 5 \times (\sqrt{2})^x$$

$$\frac{80}{5} = (\sqrt{2})^x$$ $$16 = (\sqrt{2})^x$$

We know that $\sqrt{2} = 2^{1/2}$ and $16 = 2^4$.
Substitute these into the equation:

$$2^4 = (2^{1/2})^x$$

Using the exponent rule $(a^m)^n = a^{mn}$:

$$2^4 = 2^{\frac{x}{2}}$$

Since the bases are the same, the exponents must be equal:

$$4 = \frac{x}{2}$$

Multiply both sides by 2 to solve for $x$:

$$x = 4 \times 2$$ $$x = 8$$

The value of $x$ is 8. This corresponds to option (c).

The final answer is $\text{c) 8}$.