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CGP EDU Academic Team
Published on: August 14, 2026
If ln (2x 2 - 5),ln (x 2 - l) and ln (x 2 - 3) are the first three terms of an arithmetic progression, then its fourth term is
Text Solution
Verified by ExpertsThe correct answer is:
A
ln8-ln3
Condition x 2 >3 for all logs to be defined
2 ln (x 2 - 1) = ln (2x 2 - 5) + ln (x 2 - 3)
(x 2 - 1) 2 = (2x 2 - 5) (x 2 - 3)
x 4 + 1 - 2x 2 = 2x 4 - 6x 2 - 5x 2 + 15
x 4 - 9x + 14 = 0 
x 2 = 2,7
Since, x 2 > 3 
x 2 = 7
So the numbers are 
ln 9,ln 6,ln 4
d = ln6-ln9 = ln 
fourth term = ln4 + ln 
= In 
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