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If log 3 log (3p – 2) and log (3p + 4) are in arithmetic progression, then what will be the value p?

If log 3 log (3p – 2) and log (3p + 4) are in arithmetic progression, then what will be the value p? Correct Answer log 23

As the two terms are given in arithmetic progression thus, log (3p – 2) – log 3 = log (3p + 4) – log (3p – 2). ➩ log (3p – 2) / log3 = log (3p + 4) / log (3p – 2) ➩ log 3p / log 2 log 3 = p log 3 log 4 log 2 / p log 3 ➩ p log 3 / log 2 log 3 = p log 3 log 4 log 2 / p log 2 ➩ p / log 2 = log 4 log 2 ➩ p = log 8 ➩ p = log 23

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