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Math Help - log equations?

  1. #1
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    log equations?

    I got this as a question:

    Simplify. State any restrictions on the variables.

    2 log w + (3/2) log w + (1/2) log w^2

    For this question I did this:

    2 log w + (3/2) log w + (1/2) log w^2
    2 log w + (3/2) log w + (1/2) x 2 log w
    2 log w + (3/2) log w + log w
    2 log w + (3/2) log w
    (9/2) log w

    The 2 log w + log w is still 2 log because it is multiplying by one correct and (1/2) log w^2 is 1 log because you are multiplying (1/2) by two to get one correct?
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  2. #2
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    Quote Originally Posted by Barthayn View Post
    I got this as a question:

    Simplify. State any restrictions on the variables.

    2 log w + (3/2) log w + (1/2) log w^2

    For this question I did this:

    2 log w + (3/2) log w + (1/2) log w^2
    2 log w + (3/2) log w + (1/2) x 2 log w
    2 log w + (3/2) log w + log w
    2 log w + (3/2) log w
    (9/2) log w

    The 2 log w + log w is still 2 log because it is multiplying by one correct and (1/2) log w^2 is 1 log because you are multiplying (1/2) by two to get one correct?
    HI

    \frac{9}{2}\log w is the correct simplication , you cant go beyond that .

    For the log to be defined , w\in Z^+ or in other words w>0 , try log negative sth , ur calculator will return with math error .
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  3. #3
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    I know it is. However, I do not understand why it is like that. Could you explain my steps, or explain how you would do it?
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  4. #4
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    Quote Originally Posted by Barthayn View Post
    I know it is. However, I do not understand why it is like that. Could you explain my steps, or explain how you would do it?
    you mean the steps to get (9/2)log w , or why w must be >0 ? which one ?
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  5. #5
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    Quote Originally Posted by mathaddict View Post
    you mean the steps to get (9/2)log w , or why w must be >0 ? which one ?
    I wish to understand how to do the steps to get the final answer. I understand that a negative log will give you an error. I am confused with the 1/2 log w^2
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  6. #6
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    Quote Originally Posted by Barthayn View Post


    The 2 log w + log w is still 2 log because it is multiplying by one correct and (1/2) log w^2 is 1 log (correct)because you are multiplying (1/2) by two to get one correct?
    2\log w+\log w=3\log w

    this part ?
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  7. #7
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    ahh. I see my mistake. I guess I looked at my steps incorrectly. I see I did everything correct. Thank you for your help.
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