Find the value of y, if log (y + 8) + log (y – 8) = 2log 3 + 2log 5

Step 1: Simplify right side using log power rule
2log 3 + 2log 5 = log 3² + log 5²
= log 9 + log 25

Step 2: Apply log product rule to both sides
Left: log(y + 8) + log(y – 8) = log[(y + 8)(y – 8)]
Right: log 9 + log 25 = log(9 × 25) = log 225

Step 3: Set arguments equal
(y + 8)(y – 8) = 225

Step 4: Expand left side
y² – 64 = 225
y² = 289

Step 5: Solve for y
y = ±√289
y = ±17

Note: Check y = -17 in original: log(-17 + 8) = log(-9) is undefined
Only y = 17 is mathematically valid, but given options list ±17