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# Differentiation with ln Watch

1. So I've got this question, and I've got it correct, but in the answers part of my textbook its given in a different form. Does it matter?

The question is:

Find the stationary point on the graph

$\fn_cm y=5+4x+e^{-x}$

So the differential is

$\fn_cm \frac{dy}{dx}=4-e^{-x}$

And I've worked out the stationary point to be at

$\fn_cm x=-ln(4)$

But in the textbook, its given as

$\fn_cm x=-2ln(2)$

Which to me isn't simplified because it looks more complicated‽
2. Alnx = lnx^A

so -ln4 = -ln2^2

hence following the previous rule, -ln4 = -2ln2
3. Yeah I get how it works and can see how they are equal to each other. Its just that when finding the corresponding y value, although my answer looks different to the one in the textbook, they give the same numerical answer.

$\fn_cm y=9-4ln(4)$

And theirs is

$\fn_cm y=9-8ln(2)$

Which like I have said, I know gives the same numerical answer. But does it matter that it looks different?
4. (Original post by Banny Dyrne)
Yeah I get how it works and can see how they are equal to each other. Its just that when finding the corresponding y value, although my answer looks different to the one in the textbook, they give the same numerical answer.

$\fn_cm y=9-4ln(4)$

And theirs is

$\fn_cm y=9-8ln(2)$

Which like I have said, I know gives the same numerical answer. But does it matter that it looks different?
It is good practice to reduce the number inside the ln as much as possible while keeping it as an integer.
5. Oh ok. Nice one. I'll start doing that.
6. (Original post by Banny Dyrne)
Yeah I get how it works and can see how they are equal to each other. Its just that when finding the corresponding y value, although my answer looks different to the one in the textbook, they give the same numerical answer.

$\fn_cm y=9-4ln(4)$

And theirs is

$\fn_cm y=9-8ln(2)$

Which like I have said, I know gives the same numerical answer. But does it matter that it looks different?
In your case, it really doesn't matter; they are both considered to be equally simplified. Peace.

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Updated: March 28, 2013
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