Question

Solve for x:

log (x + 6) + log (x – 6) = 2 log 8

Answer 1

We are given:

log (x + 6) + log (x – 6) = 2 log 8

Step 1: Use log addition rule

log[(x + 6)(x – 6)] = 2 log 8

Simplify:

log(x² – 36) = log 8² = log 64

Step 2: Equate the arguments of the logs

x² – 36 = 64

⇒ x² = 100

⇒ x = ±10

Step 3: Check for validity

x = 10 ⇒ log(10 + 6), log(10 – 6) → valid (positive inputs)

x = –10 ⇒ log(–10 + 6), log(–10 – 6) → invalid (log of negative numbers)

x = 10