Published by:
CGP EDU Academic Team
Published on: August 12, 2026
Using calculus , prove that log 2 3 > log 3 5 > log 4 7.
Text Solution
Verified by ExpertsThe correct answer is:
CHECK THE SOLUTION.
Let f(x) = 
for x > 1
Now f’(x) = 
Let g(x) = (2x – 1) log e (2x – 1) – 2xlog e x
⇒ g’(x) = 2log e (2x – 1) – 2log e x + 2 – 2 = 2 log e 
> 0 for x > 1
⇒ for x > 1 , we have g(x) > g(1) ⇒ g(x) > 0
⇒ f’(x) > 0 for x > 1 ⇒ f(x) is increasing for x > 1
4 > 3 > 2 ⇒ f(4) > f(3) > f(2) ⇒ 
> 
> 
.
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