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Given that log 2 3 = 1.585, find without using tables the

  1. Nov 12, 2012 #1
    Given that log2 3 = 1.585, find without using tables the

    Given that log2 3 = 1.585, find without using tables the value of


    log2 ( sin ∏/3)

    I wrote this

    log2 (0.866) but was not getting the answer in the book.
     
    Last edited: Nov 12, 2012
  2. jcsd
  3. Nov 12, 2012 #2

    Dick

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    Re: Logarithim

    You really have to make some attempt or your thread will be deleted. What's sin(pi/3)?
     
  4. Nov 12, 2012 #3
    Re: Logarithim

    I'm sorry I forgot to type my attempt! Sin of pi/3 is it not 0.866?
     
  5. Nov 12, 2012 #4

    Dick

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    Re: Logarithim

    Yes, it is approximately. But that doesn't help. Do you know an exact expression for it? That maybe might contain a 3?
     
  6. Nov 12, 2012 #5
    Re: Logarithim

    Hm.. can I convert it to degrees? and make it like 60 degrees?
     
  7. Nov 12, 2012 #6

    Dick

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    Re: Logarithim

    Yes, 60 degrees=pi/3. It's related to the sides of a 30-60-90 triangle.
     
  8. Nov 12, 2012 #7
    Re: Logarithim

    hm...... I'm not getting it .. I'm supposed to do something involving a triangle? Do something with sin∏/6, sin ∏/3, sin∏/2?
     
  9. Nov 12, 2012 #8

    Dick

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    Re: Logarithim

    If you don't remember an exact expression for sin(pi/3)=sin(60 degrees) could you try and look it up? Maybe try "30-60-90 triangle"? This really about logs, not trig functions. You don't have to derive it.
     
  10. Nov 12, 2012 #9
    Re: Logarithim

    Hm.. I see something about.. ratios of the side of the triangles 1 : 2 : root 3

    that's all
     
  11. Nov 12, 2012 #10

    Dick

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    Re: Logarithim

    Ok, since it's not a trig problem, I'll tell you sin(pi/3) is opposite side/hypotenuse. That's sqrt(3)/2 in the ratios you are looking at. Now can you do the log part?
     
  12. Nov 13, 2012 #11
    Re: Logarithim

    Oh yes I believe so. log 1/2 3- 1
     
  13. Nov 13, 2012 #12
    Re: Logarithim

    I got 1.17925 , this it written with postive mantissa
     
  14. Nov 13, 2012 #13

    HallsofIvy

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    Re: Logarithim

    I have no idea what that means.

    You had already got, before, that this is approximately log(.8660) which is no where near 1.17925. In fact, because .8660 is less than 1, its log must be negative. But the whole point of this exercise is to use the laws of logarithms to write the exact value, not a decimal approximation that you could have gotten on a calculator.

    Dick has already told you that [itex]sin(\pi/3)= \sqrt{3}/2[/itex]. Use the laws of logariths to reduce [itex]log(\sqrt{3}/2)= log(3^{1/2}/2)[/itex].
     
  15. Nov 13, 2012 #14

    SammyS

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    Re: Logarithim

    Don't forget that the logarithm you're given and the one asked for are base 2.

    You're given a value for [itex]\displaystyle \ \ \log_2(3)\,,\ \ [/itex] and from that, you're asked to find [itex]\displaystyle \ \ \log_2\left(\frac{\sqrt{3}}{2}\right)\ .[/itex]

    Use properties of logarithms to do that.
     
  16. Nov 13, 2012 #15
    Re: Logarithim

    lol I'm sooooo sorry I typed it horribly wrong in my last post. I was tired.

    I meant to type this log(3√/2)=log(3 1/2/2)= 1/2log3 - log2

    I got -0.2075
    then with positive mantissa 1.17925
     
  17. Nov 13, 2012 #16

    Dick

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    Re: Logarithim

    I'll agree with -0.2075. I'm not sure what you are on about with the 'positive mantissa'. The log is 0.7925-1. Isn't 0.7925 the mantissa?
     
  18. Nov 13, 2012 #17
    Re: Logarithm

    ehh well....... I'm too sure about the mantissa thing, my teacher didn't teach me that. I just looked in the text book and the question said express the answer with positive mantissa.

    and I think that .17925 is the postive mantissa and 1 is the character?
     
  19. Nov 13, 2012 #18

    Dick

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    Re: Logarithm

    Then you are confused. Might want to check the textbook again. The answer came out as 0.7925-1=-0.2075. 0.7925-1 is already expressed as a positive fractional part 0.7925, the mantissa, plus an integer part -1, the character. The whole mantissa/character thing is a bit of a throwback to days before computers when people used to look up logarithms in books full of tables. Your teacher is probably right to skip it.
     
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