Is ln(x^(p(x))) = p(x) ln(x)??

Uriel Hartman

Uriel Hartman

Answered question

2022-11-03

Is ln ( x p ( x ) ) = p ( x ) ln ( x )?
I am trying to prove that:
x ln ( ln ( x ) ) ln ( x ) = ln ( x )
My "solution":
e ln ( x ln ( ln ( x ) ) ln ( x ) ) = e ln ( ln ( x ) ) ln ( x ) ln ( x ) = e ln ( ln ( x ) ) = ln ( x )
Is the first step valid, i.e is ln ( x p ( x ) ) = p ( x ) ln ( x )
How can I find out for myself?

Answer & Explanation

Lena Gomez

Lena Gomez

Beginner2022-11-04Added 14 answers

x ln ( ln ( x ) ) ln ( x )
= x log x ( ln ( x ) )
= ln ( x ) log x ( x )
= ln ( x )
reevelingw97

reevelingw97

Beginner2022-11-05Added 4 answers

Given x ln ( ln x ) ln x , Now Let ln x = y x = e y
So expression convert into e y ln y y = e ln y = y = ln x
Note that ln ( x ) p ( x ) = p ( x ) ln x , Where x > 0

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