How to use this Logarithm Expression

[ptc-3873503]

 how to write this variable in PTC Mathcad prime?

[NickKemaev]

as an example

[Werner_E]

In Prime, log(x) alone stands for the decimal logarithm – unfortunately, because this does not comply with the standard and should actually be lg(x). Of course, you could also define the function yourself -> lg(x):=log(x)
In other programs, log(x) often stands for the natural logarithm, which is no better, because it should be denoted by ln(x).
Prime supports ln(x) but also logarithms to any base, because the log function can also be used with a second function argument, the logarithm base.
So you could also write the natural logarithm as log(x,e), analogous to the general notation in your image. But why would you do that when you have the ln function ready to use?

[Derbigdog]

Hi Warner,

Good reply but as an American engineer, log(x) always implied base 10 and ln(x) base "e". For a different base we used loga(x) for base "a"

[Werner_E]

But as an engineer in particular, you should be used to adhering strictly to standards, right?

Luc was faster to post the ISO 80000-2 standard dealing with logarithm.
(actually I thought that "ld" would be defined as an alias for "lb" in the standards, but obviously that's not the case).

And if you are really used to log(x) denoting the 'common' logarithm with base 10, you will have to be very careful when using programs like MatLab and Maple as in both log(x) means the natural logarithm. 😈

Wolfram is arrogant enough to define his own “standards,” but even in Mathematica, Log[x] (note the upper case "L" and square brackets) stands for the natural logarithm.

None of these programs is adhering to the standards and I wonder why - shouldn't be that difficult.

Nor do pocket calculators adhere to the standard. Here "log" usually means the base-10-log and instead of "arcsin" etc. the key is labeled with sin^-1 which is quite common use but also does not conform to the standard. Actually sin^-1(x) should be interpreted as 1/sin(x), i.e., as a reciprocal value and not as an inverse function. Similar to sin² x = (sin(x))².

[Derbigdog]

Well you learn something every day. ISO 8000-2 maybe the "new" standard. However, as a licensed, practicing engineer since the 1970's, only the first 2-12-4 and 2-12-5  reflect my experience. Now lg(x) and lb(x) are new to me. Maybe since programing has become so prevalent, the way to display logarithms has taken on these different forms. 

I still actively teach Audio engineering and Amateur Radio license courses. Still have not seen 2-12-6 and 2-12-7 used.

[StuartBruff]

Hi DBD,
What is the 2-12 that you are referring to?

FWIW, the ANSI/IEEE STD 260.3-1993 Section 9.5.2.1 defines lb, lg, and ln as symbols for the binary, decimal, and natural logarithms, respectively, and defines log as the general logarithm symbol.

Stuart

[Werner_E]

2-12-xx is referring to the ISO standards as posted by Luc here further below -> Re: How to use this Logarithm Expression - PTC Community

[StuartBruff]

But which standard?  The ISO 80000 series didn't exist in the 1970s; indeed, the 80000 series was preceded by the ISO 31 series, which itself was based on the I.U.P.A.P.-25 (1987 Revision, I believe).

Stuart

I.U.P.A.P. = International Union of Pure and Applied Physics.

https://archive2.iupap.org/wp-content/uploads/2014/05/A4.pdf

[Werner_E]

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@StuartBruff wrote:

But which standard?  The ISO 80000 series didn't exist in the 1970s;

No problem as Luc was referring to the standards existing in 2025 😉

[StuartBruff]

Yes, but @Derbigdog was referring to a 1970s standard (2-12-4), and it was the identity of that standard that I was querying.

Stuart

[Werner_E]

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@StuartBruff wrote:

Yes, but @Derbigdog was referring to a 1970s standard (2-12-4), and it was the identity of that standard that I was querying.

Stuart

---

Ah!

I understood that @Derbigdog  was referring to Luc's answer and that he was saying that, based on his experience, he only knew the terms  log_a x  and  ln x  from these current standards, but not  lg x  or  lb x.

[StuartBruff]

Ah. Right. Thanks.

I just skimmed Luc’s post, being familiar with the symbols, and thus paying no attention to the definition numbering.

It’s a good job gibbeting only applies to incorrect symbol usage and not every intimate detail of the standard!

Stuart

[Derbigdog]

You are correct Werner. I was not even aware that there were standards set for the use of the logarithmic symbols.  As a licensed practicing engineering, now retired, I had to take yearly courses to keep my license. I don't remember ever running across the lg(x) or lb(x) symbols. Of course my career was spent primarily in telecommunications and power engineering.

Now dB (decibels) is a different can of worms. There you see dB, dBrn, dBm, dBu, dBV, etc. I am in the process of writing a short tutorial, for my students, on dB that pertains to radio applications. Not sure I want to confuse things by explaining all the various forms of logarithms.

[Werner_E]

Unfortunately, I don't know since when the standards have been promoting the use of lg for log₁₀ and discouraging the use of log. Perhaps it was in the mid/late 1970s, when tangens was no longer to be denoted by tg but by tan, and zero was suddenly added to the natural numbers. The latter without great parts of the academic world having taken note of or accepted it to this day. When natural numbers are mentioned in a paper today, it is by no means clear whether zero is included or not—each author handles this as they see fit. Standards are not laws, after all, and failure to comply with them is not punishable by law.

[StuartBruff]

Whenever it was, lg has been in use in international standards for a long time, and ignorance of the standards is no excuse for failure to use the correct symbol.  If standards are not enforced, then people will feel that they can write whatever they like with impunity.  Fortunately, I'm feeling mellow today and in a forgiving mood.  Consequently, I'm in favour of just gibbeting for improper use of standards.  Well, for a first offence, anyway.  And, obviously, we'll need a control group ...

Stuart

As seen in the image below, gibbets were used to punish British mathematicians found using Leibniz's notation instead of Newton's during the Great Notation War.

Mathematicians, Ye Be Warned.

https://en.wikipedia.org/wiki/Gibbeting

https://de.wikipedia.org/wiki/Gibbeting

[StuartBruff]

There are a few other logarithm systems in general use.  Here are some, including natural and decimal, defined using Mathcad's log function.

Stuart

[LucMeekes]

This is what the internation standard (ISO 80000-2) states about notation of logarithms:

Luc