# Thread: help with natural logs

1. ## help with natural logs

I am trying to brush up on logs and I am having a hard time finding some more challenging problems. Here is an example of one.

$ln\frac{{(2x+3)^5}{\sqrt{4-sinx}}}{{(9+e^{3x})}{(9-2x)^4}}$

I am looking to practice more problems like this one. For example, what would I do if I had a third root along with the 4-sinx?

2. $\ln{\frac{{(2x+3)^5}{\sqrt[3]{4-\sin{x}}}}{{(9+e^{3x})}{(9-2x)^4}}}$

$5\ln(2x+3) + \frac{1}{3}\ln(4-\sin{x}) - \ln(9+e^{3x}) - 4\ln(9-2x)$

3. Thanks, but since you took 4-sinx out of the square root, don't you normally have to multiply that to the 1/2, so why would you then not have (1/3)(1/2)?

4. Originally Posted by gammaman
I am trying to brush up on logs and I am having a hard time finding some more challenging problems. Here is an example of one.

$ln\frac{{(2x+3)^5}{\sqrt{4-sinx}}}{{(9+e^{3x})}{(9-2x)^4}}$
Please pardon my confusion, but what are you supposed to do with this? You posted this to calculus; are you supposed to differentiate the associated function?

Thank you!

5. Oh yes, i am supposed to differentiate. However as said before I need some of the more complicated ones to practice, both diff and integration. I don't mean to beg but the ones in the text book and the ones I am finding on-line are far less complicated then the ones that will be on my test.

6. Originally Posted by gammaman
Thanks, but since you took 4-sinx out of the square root, don't you normally have to multiply that to the 1/2, so why would you then not have (1/3)(1/2)?
$\sqrt[3]{a} = a^{\frac{1}{3}}$

$\sqrt{a} = a^{\frac{1}{2}}$

see the difference?

a radical with no index is presumed to be a square root.