Question About Logs

[Christian.]

Good evening all,
For the past few days I have been confused on what Im supposed to do with logs in this set of formulas. The book says to use six or seven places of logrithms, but does not clearly say where or how to use them in the formula. I know what logs are and how to do them, its the wording of the book thats causing me trouble. Can anyone please help me to understand what to do? Thanks you.

Christian

Note: I highlighted the sections I am confused with within a yellow box. The fromula is scatterd to parts of diffrent pages. The book gives no examples for this set of formulas.

 

[ksdhart2]

Best as I can tell, "...places of logarithms" just means compute the logarithm of (whatever) in the usual manner, then round to the appropriate number of decimal places. However, this is really just a guess because you're right, the wording is poor and quite unclear. This is certainly the first I've ever heard anyone say "seven places of logarithms."

 

[Dr.Peterson]

Clearly this is a very old book, with an old style of writing and old tools for computation.

Without seeing more of it, I'm not sure whether it is just talking about using logarithms to simplify calculations (multiplication or division), which could be ignored entirely since we have calculators now; or about some specific process of "interpolating using logs". I would hope that earlier examples would demonstrate one of both of these processes.

The references to "five-place logarithms" and the like presumably mean you should use a table that gives logs with that much precision. That detail can be ignored today, as calculators give far more precision.

Can you find the first use of logs in the book, or find interpolation in the index?

 

[Christian.]

Clearly this is a very old book, with an old style of writing and old tools for computation.

Without seeing more of it, I'm not sure whether it is just talking about using logarithms to simplify calculations (multiplication or division), which could be ignored entirely since we have calculators now; or about some specific process of "interpolating using logs". I would hope that earlier examples would demonstrate one of both of these processes.

The references to "five-place logarithms" and the like presumably mean you should use a table that gives logs with that much precision. That detail can be ignored today, as calculators give far more precision.

Can you find the first use of logs in the book, or find interpolation in the index?

Thank you for helping everyone. This is the first use of logs in the book and it does not explain what to do with them anywhere on other pages, it only says to use logs. I will post the rest of the pages for this part if it helps. I agree to use a calculator. I don't understand where the logs are to be placed and used within the formula. I will note it says to use log tables, subtraction and additon log tables in the introduction.

 

[Christian.]

The other 4 pages.

 

[JeffM]

It is saying to use logs because that is how we used to do complicated arithmetic computations before calculators and computers. A modern scientific calculator will give you better answers without having to deal with what once were necessary tools but are now relics. Moreover, nowadays if you want the logarithm of a number, you use your calculator to get it. In the old days, you used log tables. I still have a book on my desk that has over a hundred pages of tables of logarithms and anti-logarithms. If you are lucky, the book gives formulas instead of all this detail about logs and interpolations. The formulas are what is important.

 

[Christian.]

It is saying to use logs because that is how we used to do complicated arithmetic computations before calculators and computers. A modern scientific calculator will give you better answers without having to deal with what once were necessary tools but are now relics. Moreover, nowadays if you want the logarithm of a number, you use your calculator to get it. In the old days, you used log tables. I still have a book on my desk that has over a hundred pages of tables of logarithms and anti-logarithms. If you are lucky, the book gives formulas instead of all this detail about logs and interpolations. The formulas are what is important.

Thank you for the reply, it was very helpfull. So basicaly I only need the formulas and the only time I have to do a log with the log button on a calculator is if it shows Log then some function?

 

[JeffM]

Thank you for the reply, it was very helpfull. So basicaly I only need the formulas and the only time I have to do a log with the log button on a calculator is if it shows Log then some function?

I am relatively confident that is the case. If not, someone here should be able to help.

 

[Dr.Peterson]

Last night, too late to do any more thinking, I found the book online (by searching for a sentence from your excerpt:

• https://books.google.com/books?id=zI45AAAAMAAJ

Scanning through it, I see a couple explanations of what is meant by interpolation (linear and quadratic); clearly this is for interpolating between values in the tables. There is a chapter that may include formulas for the tables (I haven't tried to read through it in detail); if so, you would just calculate that using modern methods and skip the tables entirely. I do see logs in some formulas. Unfortunately, it is very hard to follow much of what is said without familiarity with the methods of the time, particularly details of the kinds of tables referred to. (For example, some may actually be tables of logs of sines, or things like that.)

 

[JeffM]

Last night, too late to do any more thinking, I found the book online (by searching for a sentence from your excerpt:

• https://books.google.com/books?id=zI45AAAAMAAJ

Scanning through it, I see a couple explanations of what is meant by interpolation (linear and quadratic); clearly this is for interpolating between values in the tables. There is a chapter that may include formulas for the tables (I haven't tried to read through it in detail); if so, you would just calculate that using modern methods and skip the tables entirely. I do see logs in some formulas. Unfortunately, it is very hard to follow much of what is said without familiarity with the methods of the time, particularly details of the kinds of tables referred to. (For example, some may actually be tables of logs of sines, or things like that.)

In the book that I still have from when I was in secondary school, the log tables that I was referring to in a previous post include logs of trig functions denominated in both degrees and radians.

I think that people who graduated from college after the mid-1960's can have no appreciation of what was required to do complex calculations before the advent of scientific calculators and personal computers.

 

[Christian.]

Last night, too late to do any more thinking, I found the book online (by searching for a sentence from your excerpt:

• https://books.google.com/books?id=zI45AAAAMAAJ

Scanning through it, I see a couple explanations of what is meant by interpolation (linear and quadratic); clearly this is for interpolating between values in the tables. There is a chapter that may include formulas for the tables (I haven't tried to read through it in detail); if so, you would just calculate that using modern methods and skip the tables entirely. I do see logs in some formulas. Unfortunately, it is very hard to follow much of what is said without familiarity with the methods of the time, particularly details of the kinds of tables referred to. (For example, some may actually be tables of logs of sines, or things like that.)

Just to clear everything up concerning the overall book. Use only the formulas given in the main text and ignor the log tables and long computation tables in the examples. This should be fine and will still give the same results. Sorry if Im too confused. Thanks for all the help.