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NDA 2026 · PYQ · Logarithms · easy

If 1 − log₁₀ 2 = log₁₀(5^x + 4^x + 3^x + 2^x + 1), then what is a value of x?

Answer

The correct answer is D: 0. 1 − log₁₀ 2 = log₁₀ 10 − log₁₀ 2 = log₁₀ 5. So 5^x + 4^x + 3^x + 2^x + 1 = 5.

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

Explanation

1 − log₁₀ 2 = log₁₀ 10 − log₁₀ 2 = log₁₀ 5. So 5^x + 4^x + 3^x + 2^x + 1 = 5. Testing x = 0: 1 + 1 + 1 + 1 + 1 = 5. ✓
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