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# Log Question watch

1. I'm having a total memory blank! If you had ln(4+2^t) (t=variable) how could you expand it so that you end up with t=something!

Thanks
2. Well what does that equation equal for a start? Say it equals zero, you then know that 4 + 2^t = e^0 = 1. You then rearrange it from there.
3. (Original post by Fermat)
Use mclaurin series for ln(1+x).
Arghh! Don't know what that is (only done up to P3).

The question's off a P2 paper:

Use the model (below) to predict the no. of years needed for the population of deer to increase from 800 to 1800:

P = [2000(1.1776^t)]/(4 + 1.1776^t)
4. (Original post by Hoofbeat)
Arghh! Don't know what that is (only done up to P3).

The question's off a P2 paper:

Use the model (below) to predict the no. of years needed for the population of deer to increase from 800 to 1800:

P = [2000(1.1776^t)]/(4 + 1.1776^t)

y=ln(4 + 2^t)
e^y = 4 + 2^t
2^t = e^y - 4
tln2 = ln(e^y - 4)
t = ln(e^y - 4)/ln2
===================
5. P=2000X/(4+X), X=1.1176^t
4P + XP = 2000X
X(2000 - P) = 4P
X = 4P/(2000 - P)

take logs of both sides.
6. (Original post by Fermat)
P=2000X/(4+X), X=1.1176^t
4P + XP = 2000X
X(2000 - P) = 4
X = 4/(2000 - P)

take logs of both sides.
Fermat, which is the better anwer in terms of the one which is simplified the furthest:

2lnx or ln(x^2) ?
7. (Original post by bono)
Fermat, which is the better anwer in terms of the one which is simplified the furthest:

2lnx or ln(x^2) ?
I guess it depends what else, if anything, might be in the final answer.

If you get lots of terms with powers of x , then lnx² may look better. Just by itself, 2lnx is simpler => better.

Your answer should look good - usually this means simplified and/or elegant.
8. (Original post by Fermat)
I guess it depends what else, if anything, might be in the final answer.

If you get lots of terms with powers of x , then lnx² may look better. Just by itself, 2lnx is simpler => better.

Your answer should look good - usually this means simplified and/or elegant.
Ok.
9. (Original post by bono)
Fermat, which is the better anwer in terms of the one which is simplified the furthest:

2lnx or ln(x^2) ?
Although no one's asked me I'd say 2lnx is the fully simplified version....
10. (Original post by davey_boy)
Although no one's asked me I'd say 2lnx is the fully simplified version....
Yes, but if your answer is 2lnx + lnx² then it looks, and sounds, better as,

(lnx)² + lnx²
========

which is the square of a log plus the log of a square.
11. (Original post by Fermat)
Yes, but if your answer is 2lnx + lnx² then it looks, and sounds, better as,

(lnx)² + lnx²
========

which is the square of a log plus the log of a square.
Probably why no one asked me in the first place

Yes, I see what you're saying, and agree with it but I think this would be a very rare answer and I'm always looking at how you would then take the answer and use it in a further portion of the question. I think 2lnx is far easier to work with so would always leave it as that.
12. HOLD IT!

I thought lnX² = 2lnX and (lnX)² was just that...
13. (Original post by XTinaA)
HOLD IT!

I thought lnX² = 2lnX and (lnX)² was just that...
Incorrect.

ln(x^2) = 2lnx

There is a difference between (lnx)^2 and ln(x^2) [Or lnx^2, the brackets is optional but not necessary at all]

Observe.

Let x = 3

ln3^2 = 2ln3 = ln9 = 2.197 (4.S.F)

(ln3)^2 = (ln3)(ln3) = 1.207 (4 S.F.)
14. (Original post by XTinaA)
HOLD IT!

I thought lnX² = 2lnX and (lnX)² was just that...
This comes from another thread tina.

There was an answer there like this,

(lnx)² + lnx²

and bono just used this thread to ask me what was the better way of writing lnx², as lnx² or as 2lnx. See bono's thread above.
15. (Original post by bono)
Incorrect.

ln(x^2) = 2lnx

There is a difference between (lnx)^2 and ln(x^2) [Or lnx^2, the brackets is optional but not necessary at all]

Observe.

Let x = 3

ln3^2 = 2ln3 = ln9 = 2.197 (4.S.F)

(ln3)^2 = (ln3)(ln3) = 1.207 (4 S.F.)
That's exactly my point dumbass

Just drew ln(X²) and 2lnX in my graphical calculator: 2lnX only has values for positive X but exactly the same values as ln(X²).

Then I drew (lnX)², nothing like the previous two.
16. (Original post by XTinaA)
That's exactly my point dumbass

Just drew ln(X²) and 2lnX in my graphical calculator: 2lnX only has values for positive X but exactly the same values as ln(X²).

Then I drew (lnX)², nothing like the previous two.

2lnx = lnx^2 Which does not equal (lnx)^2

What's the problem?
17. (Original post by Fermat)
This comes from another thread tina.

There was an answer there like this,

(lnx)² + lnx²

and bono just used this thread to ask me what was the better way of writing lnx², as lnx² or as 2lnx. See bono's thread above.
Well above you wrote:
(Original post by Fermat)
Yes, but if your answer is 2lnx + lnx² then it looks, and sounds, better as,

(lnx)² + lnx²
I assume you put 2lnX = (lnX)², and this is what I'm disputing.
18. "I thought lnX² = 2lnX and (lnX)² was just that..."

I was saying how that is incorrect. What is your problem?
19. (Original post by XTinaA)
I assume you put 2lnX = (lnX)², and this is what I'm disputing.
Well, that would be incorrect.
20. (Original post by bono)

2lnx = lnx^2 Which does not equal (lnx)^2

What's the problem?
That's exactly what I said, and you told me I was incorrect

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