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

[lionely]

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

Given that log₂ 3 = 1.585, find without using tables the value oflog₂ ( sin ∏/3)

I wrote this

log2 (0.866) but was not getting the answer in the book.

 

[Dick]

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


log₂ ( sin ∏/3)

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

 

[lionely]

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

 

[Dick]

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

Yes, it is approximately. But that doesn't help. Do you know an exact expression for it? That maybe might contain a 3?

 

[lionely]

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

 

[Dick]

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

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

 

[lionely]

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

 

[Dick]

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

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.

 

[lionely]

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

that's all

 

[Dick]

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

that's all

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?

 

[lionely]

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

 

[lionely]

I got 1.17925 , this it written with positive mantissa

 

[HallsofIvy]

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

I have no idea what that means.

I got 1.17925 , this it written with positive mantissa

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 $log(\sqrt{3}/2)= log(3^{1/2}/2)$.

 

[SammyS]

...

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

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.

 

[lionely]

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

 

[Dick]

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

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?

 

[lionely]

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

and I think that .17925 is the positive mantissa and 1 is the character?

 

[Dick]

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

and I think that .17925 is the positive mantissa and 1 is the character?

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.