Calculate Natural Logarithm of 273/263

[Brunno]

Calcule: $$ln\frac{273}{263}$$

 

[Defennder]

Calcule: $$ln\frac{273}{263}$$

That doesn't make any sense. What are we supposed to evaluate it to? Isn't it already given in the simplest form?

 

[Brunno]

That doesn't make any sense. What are we supposed to evaluate it to? Isn't it already given in the simplest form?

Is it?I'm sorry I don't quite understand this...Well,could this be the answer:

$$ln3*91$$
$$ln3+ln9,1*10$$
$$ln3+ln9,1+ln10$$

According to the table of natural logs:$$ln3=1.09;ln9,1=2.2;ln10=2.3$$
So:$$ln= 1.1+2.2+2.3=5.6$$

Is it right?

 

[symbolipoint]

That doesn't make any sense. What are we supposed to evaluate it to? Isn't it already given in the simplest form?

The first question to ask is, can you reduce the rational number? The quantities are not multiples of 3 or 9. Anything else possible? If not, then either use a calculator for natural logarithm of that ratio or look in tables for log_e of the numerator minus log_e of the denominator.

 

[Brunno]

The first question to ask is, can you reduce the rational number? The quantities are not multiples of 3 or 9. Anything else possible? If not, then either use a calculator for natural logarithm of that ratio or look in tables for log_e of the numerator minus log_e of the denominator.

So,It's correct my answer,right?

 

[HallsofIvy]

You still haven't made clear what the question is!

Yes, 271= 3*91= 3*9.1*10 so ln(271)= ln(3)+ ln(9.1)+ ln(10). and, to one decimal place, ln(271)= 5.6. But what does that have to do with ln(271/263)?

 

[Brunno]

You still haven't made clear what the question is!

Yes, 271= 3*91= 3*9.1*10 so ln(271)= ln(3)+ ln(9.1)+ ln(10). and, to one decimal place, ln(271)= 5.6. But what does that have to do with ln(271/263)?

$$ln263=ln2+ln1,315+ln10+ln10$$
We have that $$ln2=0.7;ln1,3=0.26;ln10=2.3$$ The sum is equable to 5.56.

At that time I was looking for for $$ln\frac{273}{263}$$,that's equal to $$ln273-ln263$$.It answer is,by a calculator,roughly 0.0373177.

I think that's the corect way isn't it?

 

[maze]

Since 263/273 is only slightly larger than 1, you could use the taylor series expansion for x near 1. To the first power ln(1+a) ~ a, to the second ln(1+a) ~ a - 1/2a^2. These give results of .03802 and .03729 respectively. The correct answer is .03732.

Or do this:
http://www.google.com/search?hl=en&q=ln(273/263)&btnG=Search

 

[HallsofIvy]

$$ln263=ln2+ln1,315+ln10+ln10$$
We have that $$ln2=0.7;ln1,3=0.26;ln10=2.3$$ The sum is equable to 5.56.

At that time I was looking for for $$ln\frac{273}{263}$$,that's equal to $$ln273-ln263$$.It answer is,by a calculator,roughly 0.0373177.

I think that's the corect way isn't it?

Or just use your calculator to find "LN (273/263)". I still don't understand what the problem is. If the problem is just to find an (approximate) value, why break it into parts? Why not just do it directly- find 273/263 and then find the logarithm of that.

 

[Brunno]

Thankyou both guys,You were very helpful.I already got my question answered.Was just that simple!