Why is -ln x is not equal to 1/ln x? I am doing differential equation now and I need to convert them into the proper form in order to do my homogeneous differential equation. So now I just found out that -ln x is not equal to 1 / ln x. I thought it should be able to convert to ln x to the negative 1 then I can put it into the form 1/ ln x. Can anyone explain about it?

Chelsea Pruitt 2022-10-28 Answered
Why is ln x is not equal to 1 / ln x?
I am doing differential equation now and I need to convert them into the proper form in order to do my homogeneous differential equation. So now I just found out that ln x is not equal to 1 / ln x. I thought it should be able to convert to ln x to the negative 1 then I can put it into the form 1 / ln x. Can anyone explain about it?
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Answers (1)

plomet6a
Answered 2022-10-29 Author has 20 answers
Why is ln ( x ) is not equal to 1 ln ( x ) ?
Because   ln ( x ) = ln ( 1 x )   and   ln ( 1 x )   is not equal to   1 ln ( x )
In general, for most of the functions f ( x ) we don't have f ( 1 x ) = 1 f ( x )
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