# Log equation

• Nov 5th 2007, 03:04 AM
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.
• Nov 5th 2007, 03:26 AM
topsquark
Quote:

Originally Posted by GAdams
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
• Nov 5th 2007, 03:33 AM
I guess verify here means show that it is the same as?
• Nov 5th 2007, 04:00 AM
topsquark
Quote:

Originally Posted by GAdams
ln ( (e^x+1) / (x^3 + x^2) ) needs to be verified

Quote:

Originally Posted by GAdams
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