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Math Help - Evaluating logs

  1. #1
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    Evaluating logs

    Having some trouble with logs. I have attached two questions. The first question I completed and wanted a second opinion on my answer. The second question confuses me (I think it's 5)

    A)my answer is 18.287711238. I got log (subscript 2) 320000, then used the equation to change the base of the log to 10 so I could use a calculater. Is this correct?

    B)my answer is 5 (guess)


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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by math619 View Post
    Having some trouble with logs. I have attached two questions. The first question I completed and wanted a second opinion on my answer. The second question confuses me (I think it's 5)

    A)my answer is 18.287711238. I got log (subscript 2) 320000, then used the equation to change the base of the log to 10 so I could use a calculater. Is this correct?

    B)my answer is 5 (guess)


    Click image for larger version. 

Name:	logs.bmp 
Views:	36 
Size:	17.1 KB 
ID:	1540
    a) Which is it? 3200 or 320000? I get 5 for the first and 11.6439 for the second.

    b) log_55 = 1 so log_2 2^{log_55} = log_2 2 = 1

    -Dan
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  3. #3
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    Quote Originally Posted by math619 View Post
    Having some trouble with logs. I have attached two questions. The first question I completed and wanted a second opinion on my answer. The second question confuses me (I think it's 5)

    A)my answer is 18.287711238. I got log (subscript 2) 320000, then used the equation to change the base of the log to 10 so I could use a calculater. Is this correct?

    B)my answer is 5 (guess)


    Click image for larger version. 

Name:	logs.bmp 
Views:	36 
Size:	17.1 KB 
ID:	1540
    I have no time to explain long, but here is quick one way of doing your problems here.

    a) Log(to the base 2)[3200] -2Log(to the base 2)[10]
    = Log(base 2)[3200 / (10^2)]
    = Log(base 2)[32]
    = 5 -------------------------answer.

    b) Log(base 2)[2 raised to Log(base 5)[5]]
    = Log(base 2)[2 raised to 1]
    = Log(base 2)[2]
    = 1 -------------------answer.

    In about 12 to 14 hours from now I can explain any other way, including your changing into base 10 first---if you like.
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  4. #4
    Forum Admin topsquark's Avatar
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    Here's the method for a):

    log_2(3200) - 2 log_2(10)

     = log_2(3200) - log_2(10^2)

     = log_2(3200) - log_2(100)

     = log_2 \left ( \frac{3200}{100} \right )

     = log_2(32) = log_2(2^5) = 5

    -Dan
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