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    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
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    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.
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    (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)
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    (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 = Sorry, I completely misread your original q.

    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
    ===================
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    P=2000X/(4+X), X=1.1176^t
    4P + XP = 2000X
    X(2000 - P) = 4P
    X = 4P/(2000 - P)

    take logs of both sides.
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    (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) ?
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    (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.
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    (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.
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    (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....
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    (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.
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    (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 :rolleyes:

    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.
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    HOLD IT!

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

    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.
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    (Original post by XTinaA)
    That's exactly my point dumbass :rolleyes:

    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.
    What are you on about?

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

    What's the problem?
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    (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.
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    "I thought lnX² = 2lnX and (lnX)² was just that..."

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

    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 :rolleyes:
 
 
 

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