Correct layout of e^/LN/10^/LOG?

[naddy]

Since you all—okay, we—are an opiniated bunch here, I need to ask:

What is the one true sacrosanct layout of the e^, LN, 10^, LOG functions relative to each other on a calculator keypad? And which other placements are heretical abominations that call for burning at the stake?

Because, you see, even Hewlett-Packard couldn't figure it out. Different models use different combinations of shifted and unshifted keys, and there's even the groupings e^/10^ and LN/LOG. (I smell smoke.)

[rprosperi]

Clearly venturing into religious ground here, you can and should expect both quietly and outrageously religious replies.

IMHO, which is 'best' depends on what the user actually uses often - some users will never, ever use e^x and LN, while others can see no reason to even have base-10 logs at all, so how do reconcile the 'best' layout to accommodate both users?

As you note, the various design teams within HP had different views, and they could even talk to the prior teams for those insights (though anecdotal evidence suggests this was only rarely done) and so chose to implement what they thought was 'best'.

While its pretty much guaranteed no single answer will gain unanimous support, these disucssions remain interesting in they reveal sometimes very different use cases and calculating habits of the various folks that reply.

Let the religious comments commence...

[AnnoyedOne]

OK, I'll be the first to march into the church of MoHPC

I'd say that LOG and LN are slightly more commonly used so I'd make them their own keys next/near each other.

I'd then make 10^x and e^x shifted functions on those keys.

As for "heretical abominations" any variation on my layout

A1

[Johnh]

Flicking through my emulator collection....

Seems to me that just as trig functions such as sin and arcsin etc, are on the same key, then Ln and e^x should be on the same key, as should Log10 and 10^x. It's not obvious though, whether the log functions should lead, or the e^x and 10^x, and the other be a shifted key. Even just within Hp's, this varies. Voyagers have the e^ x and 10^x as primary keys, while most others before and after put the log functions as primary

It depends a bit on the general scheme of whether there is one or two shift keys. Or like in Ti58/59 a shift and and an Inv key, so that 10^x took three keys presses.

I'll manage, and I can adapt to anything logical!

[KeithB]

I don't know if the HP-71 counts, since it is really a text-completion and not a "key", but it does not have the base 10 log at all, just the confusingly named "log" and "exp".

[Maximilian Hohmann]

Hello,

in "my logic", the base functions are the logarithms and the secondary functions are the exponentials. And among them, the natural logarithm takes precedence because it is a function that is required in many fields whereas the decadic logarithm occurs rather rarily. So if I had to design a keyboard, I would put "LN" and "LOG" next to each other unshifted and "E^X" and "10^X" as their secondary functions. And from what other keyboard designers came up with, my all time preference is the TI way: "lnx" as primary function and "log" as shifted function on the same key. For the exponentials, which are not even marked on the keyboard, you have to press "INV" first.

But what do you make of this layout of a 1976 Privileg 583D-E? It does not have a shift key and the inverse trigonometric functions are just in the row of keys above the normal trigonometric functions. So far so good. Next to them are the logarithms and exponentials. But can anyone figure out why they are placed in that order? I certainly can't. When I got the calculator I first thought that someone had taken it apart and put the keys back in the wrong order. But no, they work just the way the are labelled.

Regards
Max

[KeithB]

"And among them, the natural logarithm takes precedence because it is a function that is required in many fields whereas the decadic logarithm occurs rather rarily."

Clearly, you are not an RF engineer, where the exact opposite is true.

[AnnoyedOne]

I have a wooden stake and rope ready. And wood piled. Who has matches?

A1

[Maximilian Hohmann]

Hello!

(10-23-2024 01:58 PM)KeithB Wrote:  Clearly, you are not an RF engineer, where the exact opposite is true.

I always thought RF engineers need "dB" most of the time? But I am not aware of any calculator that comes with a dB key.

Regards
Max

[AnnoyedOne]

(10-23-2024 02:51 PM)Maximilian Hohmann Wrote:  I always thought RF engineers need "dB" most of the time?

Decibels (dB) are Log10/10^x based

A1

[Matt Agajanian]

(10-23-2024 12:51 PM)Johnh Wrote:  Flicking through my emulator collection....

Seems to me that just as trig functions such as sin and arcsin etc, are on the same key, then Ln and e^x should be on the same key, as should Log10 and 10^x. It's not obvious though, whether the log functions should lead, or the e^x and 10^x, and the other be a shifted key. Even just within Hp's, this varies. Voyagers have the e^ x and 10^x as primary keys, while most others before and after put the log functions as primary

It depends a bit on the general scheme of whether there is one or two shift keys. Or like in Ti58/59 a shift and and an Inv key, so that 10^x took three keys presses.

I'll manage, and I can adapt to anything logical!

On the TI-58/59 point, I’m just curious why you find it a “yeah. I could live with that” since 10^x and e^x require an INV prefix, there’s the extra keystroke of INV which would take extra program step when a 2nd e^x or 2nd 10^x would require just a single program step.

Okay. INV is just a single extra program rather than STO 0 3 needing all three program steps on an SR-52.

[Johnh]

I dabble and/or practice proffesionally across severall engineering fields including structures, fire safety, sound and electronics. I can say that in 40 years, I have never once pressed a natural log for a real calculation that I needed! But base 10 logs come up in all of them, occasionally, or frequengly, depending what the question is. Sound and power in dB is an obvious one, which can also include dBV, where 20.Log10 is the function. Also many relationships are plotted linearly on a log scale using base 10, or as empirical equations where a base 10 log is used to express it.

But, natural logs are a more fundamental piece of maths being derived from integrating 1/x, and I know they are key in other fields. And having both is very good for learning and exploring the maths and to understand how they can be converted to each other.

[rprosperi]

(10-23-2024 01:50 PM)Maximilian Hohmann Wrote:  But what do you make of this layout of a 1976 Privileg 583D-E? It does not have a shift key and the inverse trigonometric functions are just in the row of keys above the normal trigonometric functions. So far so good. Next to them are the logarithms and exponentials. But can anyone figure out why they are placed in that order? I certainly can't. When I got the calculator I first thought that someone had taken it apart and put the keys back in the wrong order. But no, they work just the way the are labelled.

Regards
Max

How was this image attached Max, I can't see it in either Firefox or Edge (both on WIN10). The tags look OK, so I'm not sure why it's not rendering??

[dm319]

I'm going to go with putting Log and Ln on buttons and the Antilogarithms shifted. I justify it because anti- should be shifted.

For consistency '-' and '÷' should also be shifted.

[naddy]

(10-23-2024 09:13 PM)Johnh Wrote:  But, natural logs are a more fundamental piece of maths being derived from integrating 1/x, and I know they are key in other fields. And having both is very good for learning and exploring the maths and to understand how they can be converted to each other.

I use log₂ from time to time, as in "how many bits are required to encode that integer range?". That's easy enough, ln(x)/ln(2), not worth a program.

[Thomas Klemm]

(10-23-2024 10:40 PM)rprosperi Wrote:  The tags look OK, so I'm not sure why it's not rendering??

It is an external http link from within an https page.
Browsers block these for security reasons.

[Johnh]

(10-23-2024 10:52 PM)naddy Wrote:  I use log₂ from time to time, as in "how many bits are required to encode that integer range?". That's easy enough, ln(x)/ln(2), not worth a program.

Base 2 logs are also great for teaching about what a log actually is. I managed to ride with my son to the end of his high-school maths and help him with it. With base 2 logs, the graph is nice and easy to draw by hand on a piece of paper., using an x scale from say 0 to 8, and y from say -3 up to 3. eg

0.125, -3
0.25, -2
0.5, -1
1, 0,
2, 1
4, 2
8, 3

Having seen that, then log10 is easy to grasp and then with a couple more concepts, base e.

And then I recommended that he go and explain that to a friend, to cement the understanding

[toml_12953]

(10-23-2024 12:51 PM)KeithB Wrote:  I don't know if the HP-71 counts, since it is really a text-completion and not a "key", but it does not have the base 10 log at all, just the confusingly named "log" and "exp".

You can always type LOG10 or LGT for base 10 calculations.

LOG and EXP aren't confusing to BASIC programmers. We've always known that LOG and EXP use base e.

[Johnh]

(10-23-2024 09:11 PM)Matt Agajanian Wrote:  On the TI-58/59 point, I’m just curious why you find it a “yeah. I could live with that” since 10^x and e^x require an INV prefix, there’s the extra keystroke of INV which would take extra program step when a 2nd e^x or 2nd 10^x would require just a single program step.

Okay. INV is just a single extra program rather than STO 0 3 needing all three program steps on an SR-52.

Well I did live with that! A TI58 was my only calc through Cambridge and the first few years of my career.

In exchange for sometimes needing the extra key press it has the benefit of cleaning up the keyboard graphics since only one extra label is needed above each key, to allow three or even four functions to be used. And although there's an extra press it's fairly intuitive to know what the Inv button will do, nothing that needs remembering.

Screenshot attached from a ti5x emulator.

[jdebord]

In Chemistry the decimal log is most often used, such as in pH = -log[H3O+] where log is log_10

When there is a neperian logarithm (ln) it is often written as 2.3 * log