# 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 $-\mathrm{ln}x$ is not equal to $1/\mathrm{ln}x$?
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 $-\mathrm{ln}x$ is not equal to $1/\mathrm{ln}x$. I thought it should be able to convert to $-\mathrm{ln}x$ to the negative 1 then I can put it into the form $1/\mathrm{ln}x$. Can anyone explain about it?
You can still ask an expert for help

• Live experts 24/7
• Questions are typically answered in as fast as 30 minutes
• Personalized clear answers

Solve your problem for the price of one coffee

• Math expert for every subject
• Pay only if we can solve it

plomet6a
Why is $-\mathrm{ln}\left(x\right)$ is not equal to $\frac{1}{\mathrm{ln}\left(x\right)}$?
Because and is not equal to
In general, for most of the functions $f\left(x\right)$ we don't have $f\left(\frac{1}{x}\right)=\frac{1}{f\left(x\right)}$