Explanation:

Because log 2, log (2x -1) and log (2x + 3) are in an AP
2 log (2x - 1) = log 2 + log (2x + 3)
Using the power rule of log, we can write 2 log (2x - 1) = log (2x - 1)²
Therefore, we can write the equation as log (2x - 1)² = log 2 + log (2x + 3)
Using product rule, we can write the right hand side of the equation as follows:
log 2 + log (2x + 3) = log 2 (2x + 3)
The modified equation after applying the power rule and the product rule of log is log (2x - 1)² = log 2 (2x + 3)
Removing log on both sides of the equation, we get
(2x - 1)² = 2 (2x + 3)
Or 4x² - 2×2x + 1 = 2 × 2x + 6
Or 4x² - 4 × 2x - 5 = 0
Let y = 2x
So, the equation can be written as y² - 4y - 5 = 0
Factorizing, we get (y - 5) (y + 1) = 0.
So, y = 5 or y = -1
So, 2x = 5 or 2x = -1
2x cannot be negative. S, 2x = 5
If 2x = 5, expressed in terms of a log, it becomes x = log25