Solve the following equation:

log₁₀5 + log₁₀(5x + 1) = log₁₀(x + 5) + 1

Given,

⇒ log₁₀5 + log₁₀(5x + 1) = log₁₀(x + 5) + 1

⇒ log₁₀5(5x + 1) = log₁₀(x + 5) + log₁₀10

⇒ log₁₀(25x + 5) = log₁₀10(x + 5)

⇒ log₁₀(25x + 5) = log₁₀(10x + 50)

⇒ 25x + 5 = 10x + 50

⇒ 25x - 10x = 50 - 5

⇒ 15x = 45

⇒ x = 3.

Hence, x = 3.