If log x = 2.3675 and log y = 0.9750, what is the value of x+y correct to three significant figures?

 

I take it that

[math]log_x=2.3675[/math] gives

[math]x=10^{2.3675}[/math]

and that

[math]log_y=0.9750[/math]

[math]\to[/math]

[math]y=10^{0.9750}[/math]

x+y gives [math]10^{2.3675}+10^{0.9750}[/math]

Is my thinking true?

Edited August 4, 201411 yr by Chikis
fixed LaTeX errors

You have no b provided.

 

 

If log x = 2.3675 and log y = 0.9750, what is the value of x+y correct to three significant figures?

 

b^2.3675 + b^0.9750 = x+y

So your thinking is true if b is 10

Edited August 4, 201411 yr by fiveworlds

You have no b provided.

...

So your thinking is true if b is 10

When no base is given, the convention is to assume 10.

In computer science the convention is to assume 2. Though I think the final convention was to always specify. http://planetmath.org/node/70290

Realistically speaking computers can use any base from 2-64+ You can look them up.

Edited August 4, 201411 yr by fiveworlds

When no base is given, the convention is to assume 10.

That depends on the field, as already said. In physics and math, for example, it usually denotes the natural logarithm (in my experience, at least). Also see https://en.wikipedia.org/wiki/Logarithm#Particular_bases .

 

@fiveworlds: The planethmath convention may be to specify it. But I do not think that is common practice in a professional environment. Unless one explicitly means a non-standard base, of course (non-natural logarithm in my case as a natural scientist). In many cases the base should be clear from the wider context, anyways.

Edited August 4, 201411 yr by timo

That depends on the field, as already said. In physics and math, for example, it usually denotes the natural logarithm (in my experience, at least). Also see https://en.wikipedia.org/wiki/Logarithm#Particular_bases .

That's what ln is for.

That's what ln is for

Go ahead and convince the math and physics community. It's not that we do not know of the notation "ln". It's merely considered archaic by many.

 

In computer science the convention is to assume 2.

 

If that is so why does Microsoft provide the arrowed buttons?

 

 

 

You have no b provided.

 

 

I don't see how the product of two numbers by logarithms is helpful to this homework help.

Edited August 4, 201411 yr by studiot

I do not think the Microsoft Windows Calculator is really targeted at theoretical computer scientists. Hands-on computer scientists will, at least in everyday work, have to be aware of the convention their programming language gives them, anyways. In my experience that is usually log referring to the natural logarithm.

1. Can discussion of logarithm notation continue elsewhere please?

 

2. OP - which section of your text / course was this question in? ie Logs/Exponents or Significant Figures/Decimal Place/Accuracy?

 

3. Is your final line intended to be an answer or just a point on way to answer?

When no base is given, the convention is to assume 10.

So what do I do next?

My main aim of starting this thread has not been met.

Is your final line intended to be an answer or just a point on way to answer?

I feel that am not handling the question the way I should, so I need some body to help get me to the right part to get this problem solved.

I want to explore this problem more and see what will come out as the final solution. This is because the result that I get by the time I evaluate [math]10^{2.3675}+10^{0.9750}[/math] is very different from the answer key in my textbook. I want to understand what is going on. Is my approach wrong? Am I not doing it the right way? What is the problem?

Edited August 17, 201411 yr by Chikis

Well, I get 243.

What does the book say?

The book says the answer is 9.46.