Question

Solve for x:

log (2x – 3) + log 3 = log (2x + 7)

Answer 1

We are given:

log (2x – 3) + log 3 = log (2x + 7)

Step 1: Combine logs on the left

log [3(2x – 3)] = log (2x + 7)

Simplify:

log (6x – 9) = log (2x + 7)

Step 2: Equate the arguments

6x – 9 = 2x + 7

⇒ 6x – 2x = 7 + 9

⇒ 4x = 16

⇒ x = 4

Step 3: Check validity

• 2x – 3 = 8 – 3 = 5 > 0
• 2x + 7 = 8 + 7 = 15 > 0

All arguments valid.

x = 4