If log10 2, log10(2x - 1), and log10(2x + 3) are three consecutive terms of an arithmetic progression, which of the following is true?

x = log2 5

x = log2 3

x = log5 2

None of these

Given that log10 2, log10(2x - 1), and log10(2x + 3) are in AP:

2 * log10(2x - 1) = log10 2 + log10(2x + 3)

log10(2x - 1)^2 = log10(2 * (2x + 3))

(2x - 1)^2 = 2 * (2x + 3)

4x^2 - 4x + 1 = 4x + 6

4x^2 - 8x - 5 = 0

(2x + 1)(2x - 5) = 0

2x = 5 or 2x = -1 ( rejected since 2x > 0 for log(2x-1) and log(2x+3) to be defined)

2x = 5

x = log2 5