help with natural logarithm

**togo** · January 5th 2013, 12:42 PM

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

**skeeter** · January 5th 2013, 12:59 PM

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?

**Plato** · January 5th 2013, 12:59 PM

Originally Posted by togo

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

What is the question? The above is a statement:

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

**HallsofIvy** · January 5th 2013, 01:02 PM

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!

**togo** · January 6th 2013, 07:53 AM

want to integrate it.

**togo** · January 6th 2013, 08:16 AM

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.

**skeeter** · January 6th 2013, 08:45 AM

recommend you research the technique of integration by substitution

**skeeter** · January 6th 2013, 08:55 AM

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.

...

**MarkFL** · January 6th 2013, 08:57 AM

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?

**Plato** · January 6th 2013, 08:59 AM

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 $\left[\ln(x)\right]^2~?$

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