Show (ln(x^2))^2-(ln x)^2=3(ln x)^2

Fortura7i

Fortura7i

Open question

2022-08-21

Show ( ln ( x 2 ) ) 2 ( ln x ) 2 = 3 ( ln x ) 2
I read an example on integrals.
I can't see how
( ln ( x 2 ) ) 2 ( ln x ) 2 = 3 ( ln x ) 2 .

Answer & Explanation

Cristofer Briggs

Cristofer Briggs

Beginner2022-08-22Added 8 answers

Simply use the following equation:
ln ( x 2 ) = 2 ln ( x )
Victor Harris

Victor Harris

Beginner2022-08-23Added 2 answers

Alternatively,
( ln x 2 ) 2 ( ln x ) 2 = ( ln x 2 + ln x ) ( ln x 2 ln x ) = ln x 3 ln x = 3 ln x ln x = 3 ( ln x ) 2

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