how can I write (x-ln(x)) as a fraction?

Question

I thought x/ln(x), but I think that's incorrect. any help?

Answer 1

Right idea, but you're skipping ahead a bit.

First, realize that x = ln (e^x)
So what you have is ln (e^x) - ln(x)

Now you can combine the two into a fraction:
ln ((e^x)/x)

Hope that helps!

Answer 2

Note that x = ln(e^x). So, x-ln(x) = ln(e^x) - ln(x) = ln((e^x)/x), where the last part uses an identity for logarithms.

Hope this helps.