To solve the equation \( x^{54} = 243 \), we first express 243 as a power of 3:
\[ 243 = 3^5. \]
Now we can rewrite the equation:
\[ x^{54} = 3^5. \]
To solve for \( x \), we take the 54th root of both sides:
\[ x = (3^5)^{\frac{1}{54}}. \]
Using the property of exponents \((a^m)^n = a^{m \cdot n}\), we get:
\[ x = 3^{\frac{5}{54}}. \]
Now we check which of the provided responses match \( 3^{\frac{5}{54}} \):
- 27 is \( 3^3 \)
- No solution is invalid as we have a solution
- 3 is \( 3^1 \)
- 81 is \( 3^4 \)
None of these responses matches \( 3^{\frac{5}{54}} \). Therefore, based on the provided responses, the correct answer isn't listed. However, for reference, the exact solution is \( x = 3^{\frac{5}{54}} \).