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Math Help - Stuck on this log problem.

  1. #1
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    Stuck on this log problem.

    f(x)=(Ln x)2- 3Ln x

    x=2e
    ----------------------------------------------------
    (ln(2e))2-3ln(2e)

    2ln2e-3ln(2e)

    im stuck :| logs and natural logs are the most confusing thing ever


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  2. #2
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    Re: Stuck on this log problem.

    $\ln(2e)^2 = 2\ln(2e)$ is not correct.

    What is correct is

    $\ln((2e)^2)=2\ln(2e)$


    Looking at your problem.

    $f(x)=(\ln(x))^2-3\ln(x)$

    $f(2e)=(\ln(2e))^2 - 3\ln(2e)$

    this is actually in fairly simple form. You could further do the following

    $u=\ln(2e)$

    $f(2e)=u^2-3u = (u-1.5)^2-2.25 = (\ln(2e)-1.5)^2-2.25$
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  3. #3
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    Re: Stuck on this log problem.

    Quote Originally Posted by romsek View Post
    $\ln(2e)^2 = 2\ln(2e)$ is not correct.

    What is correct is

    $\ln((2e)^2)=2\ln(2e)$


    Looking at your problem.

    $f(x)=(\ln(x))^2-3\ln(x)$

    $f(2e)=(\ln(2e))^2 - 3\ln(2e)$

    this is actually in fairly simple form. You could further do the following

    $u=\ln(2e)$

    $f(2e)=u^2-3u = (u-1.5)^2-2.25 = (\ln(2e)-1.5)^2-2.25$
    I think you read my answer wrong hahaa, could you also go step by step?

    but i was given these answer choices:
    1. f(2e) = 3(ln 2)2+ ln 2 + 2
    2. f(2e) = 3(ln 2)2+5 ln 2 + 4
    3. f(2e) = (ln 2)2− ln 2 − 2
    4. f(2e) = (ln 2)2+ ln 2 + 2
    5. f(2e) = 3(ln 2)2− ln 2 − 2
    6. f(2e) = (ln 2)2−5 ln 2 − 4
    7. f(2e) = 3(ln 2)2−5 ln 2 − 4
    8. f(2e) = (ln 2)2+5 ln 2 + 4
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  4. #4
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    Re: Stuck on this log problem.

    Quote Originally Posted by chewydrop View Post
    I think you read my answer wrong hahaa, could you also go step by step?

    but i was given these answer choices:
    1. f(2e) = 3(ln 2)2+ ln 2 + 2
    2. f(2e) = 3(ln 2)2+5 ln 2 + 4
    3. f(2e) = (ln 2)2− ln 2 − 2
    4. f(2e) = (ln 2)2+ ln 2 + 2
    5. f(2e) = 3(ln 2)2− ln 2 − 2
    6. f(2e) = (ln 2)2−5 ln 2 − 4
    7. f(2e) = 3(ln 2)2−5 ln 2 − 4
    8. f(2e) = (ln 2)2+5 ln 2 + 4
    is $e$ some variable or is it the $e$ that's the base of the natural log?
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  5. #5
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    Re: Stuck on this log problem.

    Quote Originally Posted by romsek View Post
    is $e$ some variable or is it the $e$ that's the base of the natural log?
    i believe x=2e is just some variable.
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  6. #6
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    Re: Stuck on this log problem.

    Quote Originally Posted by chewydrop View Post
    i believe x=2e is just some variable.
    it disappears from the answers in your list there...
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  7. #7
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    Re: Stuck on this log problem.

    If we start with

    $f(2e)=(\ln(2e))^2 - 3\ln(2e)$

    $\ln(2e)=\ln(2)+\ln(e)=1+\ln(2)$

    so we have

    $f(2e)=(1+\ln(2))^2-3(1+\ln(2))=$

    $1+2\ln(2)+(\ln(2))^2-3-3\ln(2)=$

    $-2 - \ln(2) + (\ln(2))^2$

    which matches choice (3)
    Thanks from chewydrop
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