If log10 5 + log10 (5x + 1) = log10 (x + 5) + 1, then x is equal to:

log₁₀ 5 + log₁₀ (5x + 1) = log₁₀ (x + 5) + 1

⟹ log₁₀ 5 + log₁₀ (5x + 1) = log₁₀ (x + 5) + log₁₀ 10

⟹ log₁₀ [5 (5x + 1)] = log₁₀ [10(x + 5)]

⟹ 5(5x + 1) = 10(x + 5)

⟹ 5x + 1 = 2x + 10

⟹ 3x = 9

⟹ x = 3.