Question

I can't figure this one out: If n > 1 and y = log n x, find dy/dx.

Answer 1

Is that \[y =\log_n x\] or \[y = \log(n*x)\]or\[y = (\log n) * x\] to your understanding?

Answer 2

What do I do about the n>1 though?

Answer 3

Right now, all the matters is correctly identifying the problem :-)

Answer 4

well wouldn't it be equal to 1/x? the derivative of ln(n*x)

Answer 5

I can't see the original from here, no matter how close I get to the screen, so I'm relying on you to identify which of those appears to be the correct interpretation. They do not all give the same answer!

Answer 6

I don't know the formatting that they use is so confusing. i don't get what they mean. Do you want me to take a picture of it?

Answer 7

Sure, that would be great. From the restriction on \(n\), I think they mean that \(n\) is the base of the logarithm, but let's see...

Answer 8

yeah, it's not very clear, but the \(n\) does seem to have a lower baseline than the letters around it, so I think it is intended to be \[y = \log_n x\]

Do you remember the change of base formula for logarithms?

Answer 9

d/dx=1/xln(n)

Answer 10

well, if you mean \[\frac{dy}{dx} = \frac{1}{x \ln n}\]I would agree, but really, it should be written with parentheses around the denominator to avoid confusion with \[\frac{1}{x}\ln x\]

Answer 11

the 3rd choice in the list is the one

Answer 12

These are the answers that I have. I hope that I am doing the right problem. The formatting is really confusing on some of these problems

Answer 13

sorry, I put an x where I mean n in \[\frac{1}{x}\ln n\]

Answer 14

Oh it's okay I got what you meant

Answer 15

Thank you!

Answer 16

I try to hold myself to the same high standards of accuracy that I expect of everyone I help :-) There is little more frustrating than trying to figure out something you don't understand from something that isn't correct!

Answer 17

The reason for the restriction on \(n\), by the way, is that if we had \(n<1\) the result would have a different sign or even be a complex logarithm. For example, if \(n=\frac{1}{2}\), then \[\frac{dy}{dx} = -\frac{1}{x \ln 2}\]and if \(n = -2\) we get
\[\frac{dy}{dx} = \frac{1}{x(i\pi + \ln 2)}\]where \(i = \sqrt{-1}\)

Answer 18

I see.

Answer 19

Could you help me with one more? My school moved my deadline to next week and I still have 9 more tests to take and I don't know how to do some of the problems because I have no time to study at this point. I don't get velocity questions.

Answer 20

Though I suppose you could argue that \[\ln -2 = i\pi + \ln 2\]so the answer is still correct...

sure, what's the question?

Answer 21

I think I could probably solve it if I knew what to do.

Answer 22

\[x(t) = \int_0^t v(t)~dt\]

Answer 23

what does t represent?

Answer 24

time!

Answer 25

that is what I thought. just making sure. haha

Answer 26

I suppose I should have written \(s(t)\) instead of \(x(t)\) to match their nomenclature...

Don't forget that you have to adjust your answer to account for the fact that you didn't start at position 0.