Question

If log₁₀√(1 + x) + 3log₁₀√(1 - x) = log₁₀√(1 - x²) + 2. Find x.

Answer 1

log₁₀(x + 1)^1/2 + log₁₀(1 – x)^3/2 = log₁₀(1 – x²)^1/2 + log¹⁰⁰10 

⇒ (x + 1)^1/2(1 – x)^3/2 = (1 – x²)^1/2 – 100 

⇒ √(1 - x²) (1 – x – 100) = 0 ⇒ x = ±1. x = -99 

But x ≠ ± 1, -99 

∴ There is no value of x exists.