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Select the correct answer to the following equation: x54=243

.(1 point)
Responses

81
81

3
3

27
27

no solution

1 answer

To solve the equation \( x^{54} = 243 \), we can rewrite 243 in terms of powers of 3.

We know that: \[ 243 = 3^5 \]

So, we can rewrite the equation as: \[ x^{54} = 3^5 \]

To solve for \( x \), we can express \( x \) in terms of a power: \[ x = 3^{\frac{5}{54}} \]

Now, we can see whether any of the provided options can be the solution of this equation:

  1. 81 can be expressed as \( 3^4 \) (not a solution).
  2. 3 can be expressed as \( 3^1 \) (not a solution).
  3. 27 can be expressed as \( 3^3 \) (not a solution).
  4. no solution is incorrect since we have found \( x = 3^{\frac{5}{54}} \).

Since none of the options match \( x = 3^{\frac{5}{54}} \), and based on our analysis, the correct answer would be "no solution" according to the given options.