This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Step 1: Apply the logarithm property a + b = (ab) for a>0, b>0. [(x+1)(x-1)] = 3 Step 2: Since is one-to-one, equate the arguments. (x+1)(x-1) = 3 Step 3: Expand the left side. x^2 - 1 = 3 Step 4: Solve for x^2. x^2 = 4 x = ± 2 Step 5: Determine the domain where both arguments are positive: x+1 > 0 and x-1 > 0. x > 1 Step 6: Check candidate solutions in the domain. For x=2 > 1: valid. Verify: (3) + (1) = 3 + 0 = 3. For x=-2 < 1: (-1) undefined in reals. Invalid. Final answer x=2