Apply the logarithm property a + b = (ab).

Step 1: Apply the logarithm property a + b = (ab). The given equation is: (x+3) + (x+5) = 15 Using the property, we combine the terms on the left side: ((x+3)(x+5)) = 15 Step 2: Equate the arguments of the logarithms. Since the natural logarithm is a one-to-one function, if A = B, then A=B. (x+3)(x+5) = 15 Step 3: Expand and solve the quadratic equation. Expand the left side: x^2 + 5x + 3x + 15 = 15 x^2 + 8x + 15 = 15 Subtract 15 from both sides: x^2 + 8x = 0 Factor out x: x(x+8) = 0 This gives two potential solutions: x = 0 or x+8 = 0 x = -8 Step 4: Check the validity of the solutions based on the domain of the natural logarithm. For (x+3) to be defined, x+3 > 0 x > -3. For (x+5) to be defined, x+5 > 0 x > -5. Both conditions must be satisfied, so we need x > -3. Let's check our potential solutions: • For x=0: 0 > -3. This condition is satisfied. Substituting x=0 into the original equation: (0+3) + (0+5) = 3 + 5 = (3 × 5) = 15. This is correct. So, x=0 is a valid solution. • For x=-8: -8 > -3. This condition is NOT satisfied. Substituting x=-8 into the original equation would give (-8+3) = (-5) and (-8+5) = (-3), which are undefined in the set of real numbers. So, x=-8 is not a valid solution. Therefore, the only valid solution is x=0. Step 5: Select the correct option. Based on our analysis, the correct option is A. The final answer is A) x=0 only. Send me the next one 📸