1. ## Log equation

Hello

ln ( (e^x+1) / (x^3 + x^2) ) needs to be verified

So here's what I got:

= ln ( (e^x+1) / (x^3 + x^2) )

= ln (e^x+1) - ln (x^3 + x^2)

= (x+1) ln e - ln ((x^2(x+1))

-can't get past this point.

Hello

ln ( (e^x+1) / (x^3 + x^2) ) needs to be verified

So here's what I got:

= ln ( (e^x+1) / (x^3 + x^2) )

= ln (e^x+1) - ln (x^3 + x^2)

= (x+1) ln e - ln ((x^2(x+1))

-can't get past this point.
What do you mean by "verified?"

We can go a few more steps:
$\displaystyle = (x+1) ln(e) - ln (x^2(x+1))$

$\displaystyle = (x+1) ln(e) - ln (x^2) - ln(x+1)$

$\displaystyle = (x+1) ln(e) - 2ln (x) - ln(x+1)$

and since $\displaystyle ln(e) = 1$,

$\displaystyle = (x+1) - 2ln (x) - ln(x+1)$

-Dan

3. I guess verify here means show that it is the same as?

ln ( (e^x+1) / (x^3 + x^2) ) needs to be verified
I guess verify here means show that it is the same as?
Show it is the same as what? I suspect the problem is asking you to simplify the expression. Something is very wrong in the terminology or there is something more to this question.

-Dan