If \( 1 - \log_{10} 2 = \log_{10}(5^x + 4^x + 3^x + 2^x + 1) \), then what is a value of \( x \) ?

  1. A. 10
  2. B. 5
  3. C. 1
  4. D. 0

Correct Answer: D. 0

Explanation

1 - \log_{10} 2 simplifies to \log_{10} 5. Equating the arguments gives 5^x + 4^x + 3^x + 2^x + 1 = 5. Substituting x = 0 makes the sum 1 + 1 + 1 + 1 + 1 = 5, satisfying the equation.

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