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

1. Nov 12, 2012

### lionely

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. Nov 12, 2012

### Dick

Re: Logarithim

You really have to make some attempt or your thread will be deleted. What's sin(pi/3)?

3. Nov 12, 2012

### lionely

Re: Logarithim

I'm sorry I forgot to type my attempt! Sin of pi/3 is it not 0.866?

4. Nov 12, 2012

### Dick

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?

5. Nov 12, 2012

### lionely

Re: Logarithim

Hm.. can I convert it to degrees? and make it like 60 degrees?

6. Nov 12, 2012

### Dick

Re: Logarithim

Yes, 60 degrees=pi/3. It's related to the sides of a 30-60-90 triangle.

7. Nov 12, 2012

### lionely

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?

8. Nov 12, 2012

### Dick

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.

9. Nov 12, 2012

### lionely

Re: Logarithim

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

that's all

10. Nov 12, 2012

### Dick

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?

11. Nov 13, 2012

### lionely

Re: Logarithim

Oh yes I believe so. log 1/2 3- 1

12. Nov 13, 2012

### lionely

Re: Logarithim

I got 1.17925 , this it written with postive mantissa

13. Nov 13, 2012

### HallsofIvy

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 $sin(\pi/3)= \sqrt{3}/2$. Use the laws of logariths to reduce $log(\sqrt{3}/2)= log(3^{1/2}/2)$.

14. Nov 13, 2012

### SammyS

Staff Emeritus
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 $\displaystyle \ \ \log_2(3)\,,\ \$ and from that, you're asked to find $\displaystyle \ \ \log_2\left(\frac{\sqrt{3}}{2}\right)\ .$

Use properties of logarithms to do that.

15. Nov 13, 2012

### lionely

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

16. Nov 13, 2012

### Dick

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?

17. Nov 13, 2012

### lionely

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?

18. Nov 13, 2012

### Dick

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.