Let's solve the given equation step-by-step:

The equation is:
$\log_{\sqrt{3}} x - 8 = 0$

Step 1: Isolate the logarithmic term

Add 8 to both sides:
$\log_{\sqrt{3}} x = 8$

Step 2: Rewrite in exponential form

Recall the logarithmic rule:
$\log_a b = c \implies b = a^c$
Here, $a = \sqrt{3}$, $c = 8$, and $b = x$.
So,
$x = (\sqrt{3})^8$

Step 3: Simplify $(\sqrt{3})^8$

The square root of 3 can be written as $3^{1/2}$. Therefore:
$(\sqrt{3})^8 = (3^{1/2})^8 = 3^{8/2} = 3^4$
And $3^4 = 81$.

Final Answer:

$x = 81$

The correct choice is:
$\boxed{x = 81}$

Do you want further details or have any questions about this solution?

Related Questions:

1. What are the general rules for converting between logarithms and exponents?
2. How can you solve logarithmic equations with different bases?
3. What is the importance of understanding fractional exponents in logarithms?
4. How would the solution change if the base were $2$ instead of $\sqrt{3}$?
5. Can you graph $y = \log_{\sqrt{3}} x$ and interpret the solution visually?

Tip: Always check your logarithmic solutions to ensure they are within the domain of the logarithmic function!