Maths - Logs

B_Fanatic

Hey, this is the first time I've ever come across a question like this and was wondering if anyone could help. Not a biggie, just what do you do when:

Squaring logs. (log[1+x])^2

Do I square the (1+x) so that it is log([1+x]^2)? Or do I treat it as two logs multiplying? If so, what the hell can I do with two multiplying logs? (If it's possible that is)

Patriciamc93

Is not put equal to anything?

B_Fanatic

Patriciamc93 wrote: »

Is not put equal to anything?

What? The equation is a differentiation one and the to be quared log above is the v^2 part of the quotient rule if that helps

Colm92

B_Fanatic wrote: »

Hey, this is the first time I've ever come across a question like this and was wondering if anyone could help. Not a biggie, just what do you do when:

Squaring logs. (log[1+x])^2

Do I square the (1+x) so that it is log([1+x]^2)? Or do I treat it as two logs multiplying? If so, what the hell can I do with two multiplying logs? (If it's possible that is)

Could we have the rest of the question?

It could have been something like (log[1+x])^2 - log[1+x] = 0?

In which case we could let log[x+1] equal to y and then solve putting back it log[x+1] after we find y. Which in this case is equal to 0 and 1.

Patriciamc93

B_Fanatic wrote: »

What? The equation is a differentiation one and the to be quared log above is the v^2 part of the quotient rule if that helps

Well if it were me I would take it that the squared only applies to the (1+x) and so you could bring it down in front to make 2log(1+x) .

I could be wrong though.... Probably am!

B_Fanatic

Dy/Dx = [ln(1+x) + 1]/([In(1+x)]^2)... Log to the base 'e' is the natural log, isn't it?

Patriciamc93

I got it to :
__1___ + ____1____
Ln(1+x). Ln(1+x)^2

Any good to you?

ShonyBoulders

Patriciamc93 wrote: »

Well if it were me I would take it that the squared only applies to the (1+x) and so you could bring it down in front to make 2log(1+x) .

I could be wrong though.... Probably am!

I'm pretty sure you're correct here, and B Fanatic, you're right in saying that log to the base "e" is the natural log. Could we have the original question?

EDIT: Did some work, which I'm not sure is right, but here we go anyway.

Taking Patricia's result, we can rewrite that as:

-ln(1+x) - 2ln(1+x)

And not completely certain, but could we tidy that up to give us :

ln(1+x)[-1-2] =
-3ln(1+x)



I'm seriously rusty on logs, so do correct me if I'm wrong.

arboroia

So:


And the derivative is:


But yet again, what is the question?

EDIT:

@shonyboulders The law you are using only applies if the power is inside of the log, but not outside.

B_Fanatic

Haha, took one last long hard look at the question there and I solved the problem. Turns out I'm a dumbass! I used quotient rule instead of product, so it's understandable that it's pretty difficult to solve it to anything reasonable. Sorry about that : P

I probably should have realised I made an error when it became anyway hard : /

Edit: http://examinations.ie/archive/markingschemes/2010/LC003ALP000EV.pdf If you want to have a look at it anyway it's question 7 (C).

ShonyBoulders

arboroia wrote: »

@shonyboulders The law you are using only applies if the power is inside of the log, but not outside.

Alright cheers mate, I'll definitely need to have another look over logs before the LC.

Patriciamc93

B_Fanatic wrote: »

Haha, took one last long hard look at the question there and I solved the problem. Turns out I'm a dumbass! I used quotient rule instead of product, so it's understandable that it's pretty difficult to solve it to anything reasonable. Sorry about that : P

I probably should have realised I made an error when it became anyway hard : /

Edit: http://examinations.ie/archive/markingschemes/2010/LC003ALP000EV.pdf If you want to have a look at it anyway it's question 7 (C).

Better to make mistakes now than on Friday!

arboroia

ShonyBoulders wrote: »

Alright cheers mate, I'll definitely need to have another look over logs before the LC.

No Problem - and remember every single log law is in the log tables, just make sure to ask for a copy - see page 21!