Solve the following logarithmic equation: 2log₁₀x + log₁₀3 = log₁₀75.

Combine the logs. 2log₁₀x = log₁₀x², so the left side is log₁₀(3x²). Then log₁₀(3x²) = log₁₀75 gives 3x² = 75.

x² = 25, so x = 5 or x = -5.

You can only take the log of a positive number. So x = -5 is not allowed, and the only solution is x = 5, with x ≠ -5. The tempting answers with x = 0 fail because log₁₀0 does not exist.