# help with natural logarithm

• January 5th 2013, 12:42 PM
togo
help with natural logarithm
question:

ln(x^2)/ln(e^x)

I just don't see anything on the formula sheet that matches this.

List of integrals of logarithmic functions - Wikipedia, the free encyclopedia
• January 5th 2013, 12:59 PM
skeeter
Re: help with natural logarithm
I assume you wish to integrate this expression?

$\frac{\ln(x^2)}{\ln(e^x)}} = \frac{2\ln{x}}{x}$

$\int 2\ln{x} \cdot \frac{1}{x} \, dx$

integration by substitution ...

let $u = \ln{x}$

can you finish?
• January 5th 2013, 12:59 PM
Plato
Re: help with natural logarithm
Quote:

Originally Posted by togo
question:
ln(x^2)/ln(e^x)

What is the question? The above is a statement:

$\frac{\ln(x^2)}{\ln(e^x)}=\frac{2\ln(x)}{x}$.
• January 5th 2013, 01:02 PM
HallsofIvy
Re: help with natural logarithm
I don't see a question! You give an expression. What do you want to do with it? If you are trying to "simplify" it then two basic properties should help: $ln(x^2)= 2ln(x)$ and [tex]ln(e^x)= x[/itex].

You give a link to a "list of integrals". Do you want to integrate that? $2\int [ln(x)/x] dx$? Then I think the substitution u= ln(x) will do nicely!
• January 6th 2013, 07:53 AM
togo
Re: help with natural logarithm
want to integrate it.
• January 6th 2013, 08:16 AM
togo
Re: help with natural logarithm
yeah I have no idea where to find the rule for handling that. It didn't look like it was on the wikipedia formula sheet.
• January 6th 2013, 08:45 AM
skeeter
Re: help with natural logarithm
recommend you research the technique of integration by substitution
• January 6th 2013, 08:55 AM
skeeter
Re: help with natural logarithm
Quote:

Originally Posted by togo
yeah I have no idea where to find the rule for handling that. It didn't look like it was on the wikipedia formula sheet.

...
• January 6th 2013, 08:57 AM
MarkFL
Re: help with natural logarithm
Quote:

Originally Posted by skeeter
I assume you wish to integrate this expression?

$\frac{\ln(x^2)}{\ln(e^x)}} = \frac{2\ln{x}}{x}$

$\int 2\ln{x} \cdot \frac{1}{x} \, dx$

integration by substitution ...

let $u = \ln{x}$

can you finish?

Do you see how this sets you up quite nicely?
• January 6th 2013, 08:59 AM
Plato
Re: help with natural logarithm
Quote:

Originally Posted by togo
yeah I have no idea where to find the rule for handling that. It didn't look like it was on the wikipedia formula sheet.

What is the derivative of $\left[\ln(x)\right]^2~?$