Question

Solve for x:

log (x + 3) + log (x – 3) = 3 log 2 + log 5

Answer 1

We are given:

log(x + 3) + log(x – 3) = 3 log 2 + log 5

Step 1: Use log properties

Left side:

log[(x + 3)(x – 3)] = log(x² – 9)

Right side:

3 log 2 + log 5 = log(2³) + log 5

= log 8 + log 5

= log(8 · 5)

= log 40

Step 2: Equate arguments

x² – 9 = 40

⇒ x² = 49

⇒ x = ±7

Step 3: Check validity

x = 7 ⇒ x + 3 = 10, x – 3 = 4 → valid

x = –7 ⇒ x – 3 = –10 → invalid (log of negative number)

x = 7