Logarithms and Anti-logarithms

[Xenophon PCDGS]

Sixty five years ago in 1956, I was in the Upper Third at St Bede's College in Manchester and our mathematics teacher was at pains to stress how the comprehension of these would be needed in our later lives. Whilst I did receive a First in Mathematics at Manchester University in 1966, I have never forgotten those words of our teacher and wonder if there are contributors on this website who were introduced to these at age 11 and if they used them in their later lives in employment.

 

[edwin_m]

I was taught them in 1978-1980 and I think they were on the syllabus for the Scottish O grade I did in 1981. But I've never used them since despite a career in engineering. A nearby sixth-former advises they are still on the maths A-level syllabus, but obtained by pressing a button on a calculator not by poring through a book of tables.

The think I never had to do was use a slide rule.

 

[Mcr Warrior]

Nope. Electronic calculators had by then become available. Thank you Mr. Casio.

 

[gg1]

I only studied Maths to GCSE level (taken in 1991) and have no memory at all of antilogarithms. Maybe something which was dropped from the syllabus with the changeover from O level to GCSE?

 

[John Webb]

I started at a comprehensive technical secondary school in 1957. I don't recall when we moved onto log and anti-log tables. I left for the local polytechnic after A-levels in 1964 to do a Physics degree and continued with logs and anti-logs and slide-rules. But on starting work in industry either slide-rules or calculators (mostly mechanical) were the norm, although I ended up introducing my test laboratory to an on-line (teleprinter) computing service which speeded things up considerably. After a couple of years (1969) I moved to a government research laboratory with computing facilities and I don't think I ever looked up logs or anti-logs again.

Added: I do have a book of statistical function tables lurking about - it took a bit longer for calculators to start getting these 'built-in' for easy use!

 

[Caboose Class]

As a retired Chemist, I still remember that the log of 760 mm Hg is 2.8808

 

[swt_passenger]

I was taught them in 1978-1980 and I think they were on the syllabus for the Scottish O grade I did in 1981. But I've never used them since despite a career in engineering. A nearby sixth-former advises they are still on the maths A-level syllabus, but obtained by pressing a button on a calculator not by poring through a book of tables.

The think I never had to do was use a slide rule.

Log tables and slide rules were still big things when I did O level in 1971, and during my engineering ONC in the 70s I used a fairly complex slide rule, and log tables, but I think both were relegated to the bottom drawer by about 1980. But I remember using log/log graph paper when checking certain equipment performance into the mid 90s, before built in analysis replaced it.

 

[Calthrop]

I'm by nature pretty innumerate; at school, anything arithmetical / mathematical was always a torment to me. Doing GCE O Levels in the early 1960s, I just scraped a pass in Elementary Maths -- which meant having, the following year, to do Additional Maths; the exam to be taken at the end of that year. Additional Maths included trigonometry, mechanics, and calculus. I (then aged 15) managed to get a bit of a "handle" on trigonometry; its processes impressed me as rather elegant -- but as for the other two categories, the stuff could have been in the Quechua language for all that it meant to me: I found logarithms utterly impenetrable. Needless to say, I failed the Additional Maths exam. Equally needless to say, I never made any use of logarithms in my working life...

The think I never had to do was use a slide rule.

Slide rules were a big thing when I did O level in 1971, and during my engineering ONC in the 70s I used a fairly complex slide rule, and log tables, but I think both were relegated to the bottom drawer by about 1980.

I recall that in Robert A. Heinlein's science fiction, he had a bit of a recurring thing about sardonic-scientist characters who expressed the opinion that anyone who could not use a slide rule, should not be allowed to vote -- but IMO, though much of Heinlein's writing is for sure, entertaining; he came out with a lot of thoroughly idiotic things.

 

[DynamicSpirit]

I was taught them in 1978-1980 and I think they were on the syllabus for the Scottish O grade I did in 1981. But I've never used them since despite a career in engineering. A nearby sixth-former advises they are still on the maths A-level syllabus, but obtained by pressing a button on a calculator not by poring through a book of tables.

The think I never had to do was use a slide rule.

Pretty much the same for me (although in England, not Scotland). I guess the early 80s were a time when the advent of cheap calculators were just rendering logarithms obsolete as a tool for doing multiplication, but they hadn't yet left the syllabus.

The thing about logarithms though is that they are incredibly useful if you see them, not as a tool for multiplication, but as a way to understand (a) very large and very small numbers, and more importantly, (b) exponential/geometric growth and decay. For example, plotting log(GDP) instead of actual GDP over time gives you a much better visualization of how actual growth rates of the economy have varied over the years. Maybe that requires a bit more than 'O'-level/GCSE maths though?

 

[cornishjohn]

maths o level with slide rule in 1982. Don't use tables as such, but calculating dB in my line of work is involving logs.

 

[ABB125]

I finished A-level further maths in 2020 (most people in the class didn't bother finishing!) and I don't recall antilogarithms ever being specifically mentioned. However, if antilogarithms are the 10^x things (eg: if log(10)100=2, then 10^2=100), we did cover them. I don't recall anything being said about them being very important in later life. (Indeed, all the teachers were if the view that "it's just maths for the sake of maths".)

 

[jfollows]

Sixty five years ago in 1956, I was in the Upper Third at St Bede's College in Manchester and our mathematics teacher was at pains to stress how the comprehension of these would be needed in our later lives. Whilst I did receive a First in Mathematics at Manchester University in 1966, I have never forgotten those words of our teacher and wonder if there are contributors on this website who were introduced to these at age 11 and if they used them in their later lives in employment.

I was taught logarithms in about 1975 (maybe earlier) at Manchester Grammar School and went on to read Mathematics at Oxford University - unlike you I didn't complete my degree there though!
I used logarithms in my mathematics O-level in 1977 along with a slide rule.
An understanding of what logarithms are has been fundamental to my understanding of the way the world works. In my last job, at one of the UK's research councils (STFC), being able to understand presentations by scientists which automatically included reference to logarithms was helpful. As you know, the fact that "natural logarithms" (to the base e rather than base 10) fall out of many mathematical constructs pretty much automatically is significant.
But as to "using" logarithms in the form of tables as an aid to calculation, no, never, good in theory but very much overtaken by the reality of calculators and computers by about 1980 I guess.

 

[swt_passenger]

I was taught logarithms in about 1975 (maybe earlier) at Manchester Grammar School and went on the read Mathematics at Oxford University - unlike you I didn't complete my degree there though!
I used logarithms in my mathematics O-level in 1977 along with a slide rule.
An understanding of what logarithms are has been fundamental to my understanding of the way the world works. In my last job, at one of the UK's research councils (STFC), being able to understand presentations by scientists which automatically included reference to logarithms was helpful. As you know, the fact that "natural logarithms" (to the base e rather than base 10) fall out of many mathematical constructs pretty much automatically is significant.
But as to "using" logarithms in the form of tables as an aid to calculation, no, never, good in theory but very much overtaken by the reality of calculators and computers by about 1980 I guess.

I remember having been given a set of log tables at school we were advised to put a big red line through the base e pages because they wouldn’t be relevant to our needs at that time. I suppose accidentally using the wrong tables must have led to some sort of confusion.

For our younger readers though, I think it’s possibly worth mentioning that a typical book of tables also included trig functions, sin cos tan etc etc, (in addition to the logs and anti logs) and they would possibly get far more day to day use at school?

 

[najaB]

...and wonder if there are contributors on this website who were introduced to these at age 11 and if they used them in their later lives in employment.

Yes (though around age 13), and no. Not even once.

 

[jfollows]

I've remembered an actual example from my work.

I was once involved in specifying a computer system which was procured through a competitive tender process. So I was the technical architect or somesuch.

In order to be accepted and paid for, it had to run a number of acceptance tests using reasonably well-known synthetic benchmarks, including but not limited to the Linpack/HPL benchmark used to rank computers on the "Top 500" list.

The final score was determined by an algorithm which included a lot of "e to the power x" specifications (so, antilogarithms to the base e), and if I recall correctly the winning bidder (us) had to specify a score and then match or exceed that score in reality.

I was able to understand that the logic behind the scoring gave significant weight to over-performance as well as significant penalties to under-performance, when compared to more simple "straight line" scores.

I was also confident that one of the benchmark acceptance tests we were going to over-perform by a significant margin, and so the "e to the power x" scoring for that result awarded us so many scoring points that we could hardly fail to match or exceed the aggregate score for all tests.

I'm not sure that many others with whom I worked understood this, but I was able to say something like "it'll be OK, trust me" and it was - we exceeded the score requirement significantly and the system was accepted and paid for.

Now that's not log tables of course, but an understanding of how logarithms worked was fundamental to my understanding and my ability to reassure my colleagues at the time.

 

[TXMISTA]

Final year MEng student here. I’ve never heard of an antilogarithm until now. I use logarithms and exponentials almost every day though.

Edit: from a quick google I’m familiar with the method but have never heard the term before

 

[Ediswan]

I finished A-level further maths in 2020 (most people in the class didn't bother finishing!) and I don't recall antilogarithms ever being specifically mentioned. However, if antilogarithms are the 10^x things (eg: if log(10)100=2, then 10^2=100), we did cover them.

Correct. AFAIR, the term 'anti-logarithm' was only ever used to describe the printed tables. Teaching logarithms without also convering the inverse function would be ... weird.

 

[ABB125]

Correct. AFAIR, the term 'anti-logarithm' was only ever used to describe the printed tables. Teaching logarithms without also convering the inverse function would be ... weird.

I thought so, but we were taught them as "inverse" functions rather than "anti"; the same goes for trigonometry and hyperbolic functions. Not to be confused with reciprocals, of course!

 

[Dent]

Correct. AFAIR, the term 'anti-logarithm' was only ever used to describe the printed tables. Teaching logarithms without also convering the inverse function would be ... weird.

I don't recall the term "anti-logarithm" being used when I studies A-Level Maths. It always seemed a silly "wrong way round" term anyway, the exponential function is more intuitive and the logarithm is defined as its inverse.

It must be a long time since logs were taught at 11, by around 2000 they were not mentioned until A-Level.

 

[Ediswan]

It must be a long time since logs were taught at 11, by around 2000 they were not mentioned until A-Level.

Before electronic caculators became commonly available, logarithms were taught as a tool for long multiplication, division etc. Especially if this was part of trigonometric calculation where you could use 'log sin' and similar tables to do two operations in one.

A separate set of anti-log tables is a luxury. You can do the same by using log tables in reverse.

Using log tables for numbers between 0 and 1 requires some notational gymnastics called 'bar notation'.

 

[edwin_m]

I don't recall the term "anti-logarithm" being used when I studies A-Level Maths. It always seemed a silly "wrong way round" term anyway, the exponential function is more intuitive and the logarithm is defined as its inverse.

It must be a long time since logs were taught at 11, by around 2000 they were not mentioned until A-Level.

I'm guessing the term "anti-logarithm" died out because the relevant button on a calculator is usually called "INV", and also does the inverse of various other functions that have never been referred to as "anti". Perhaps "anti" was a particular British term that's been subsumed by general Americanisation (or "Americanization" as this browser wants to spell it...)?

 

[jfollows]

Before electronic caculators became commonly available, logarithms were taught as a tool for long multiplication, division etc. Especially if this was part of trigonometric calculation where you could use 'log sin' and similar tables to do two operations in one.

Absolutely, at the age of 11-13 I was especially taken with the ability to calculate square roots, and so on, using logarithms. It seemed almost magical at the time.

 

[Xenophon PCDGS]

I'm guessing the term "anti-logarithm" died out because the relevant button on a calculator is usually called "INV", and also does the inverse of various other functions that have never been referred to as "anti". Perhaps "anti" was a particular British term that's been subsumed by general Americanisation (or "Americanization" as this browser wants to spell it...)?

Remember that I said it was 1956 when the subject was broached at my secondary educational establishment, which seems almost a generation before other contributors to this thread talked of their school experience of the said matter.

 

[Ediswan]

Absolutely, at the age of 11-13 I was especially taken with the ability to calculate square roots, and so on, using logarithms. It seemed almost magical at the time.

Again, luxury. Square roots can be done by hand.

 

[edwin_m]

Remember that I said it was 1956 when the subject was broached at my secondary educational establishment, which seems almost a generation before other contributors to this thread talked of their school experience of the said matter.

Indeed it is, but you were asking for the experience of others without specifying when. The concensus seems to be that log tables and the term "anti-logarithm" died out about 1980 but the concept is still taught.

 

[ac6000cw]

I learnt how to use logs and slide rules in the early 1970's at secondary school, but by the time I left in 1976 pocket 'scientific' calculators were affordable (so that was the end of my use of log tables and slide rules).

But working as an electronics engineer, I use logs and inverse logs/exponential functions frequently, so it's been very important knowledge for me (and doubtless many other engineers and scientists).

 

[AlterEgo]

I did GCSE Mathematics in 2002 and could not tell you what an anti-logarithm is.

 

[Caboose Class]

For those unfamiliar with Anti-logarithms, here is a set taken from "Physical and Mathematical Tables" by Yarwood & Castle, First Edition 1958

 

[Xenophon PCDGS]

For those unfamiliar with Anti-logarithms, here is a set taken from "Physical and Mathematical Tables" by Yarwood & Castle, First Edition 1958
View attachment 104658

Thanks for the view of these tables, first seen by me at secondary school (Upper Third) in 1956.

 

[AM9]

Wow! Seeing those images took me back to early '60s O-level maths. Strangely, most of us then new how to use log tables then, but it was at college with A1 maths that I learnt why log tables work that way. That's when the whole area of using logarithmic relationships became interesting. As everybody else has said, then calculators came along and made us abandon them, but log law plots, electronic conversion and measurment meant a lot more to me forever.