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+--- Thread: logₓy (/thread-12171.html)
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logₓy - cdmackay - 01-12-2019 09:09 PM
hi all,
I had cause to work out log₂ of a number today, and was vaguely surprised that I couldn't find it on my calculators, not even as a function, let alone on a key. Nor the more general logₓy.
The WP 34S is to be congratulated for having both on keys, but I can't find either even as a function on my DM42 or HP 50g.
It's trivial to write my own fn for e.g LOGy(x) (e.g. LOG SWAP LOG ÷), but am I missing something?
RE: logₓy - pier4r - 01-12-2019 09:12 PM
No, I think it is wanted. The log in different bases are not often used, compared to log_e and log_10 , therefore for other bases you are on your own.
you can contribute here:
http://www.hpmuseum.org/forum/thread-10271.html
RE: logₓy - cdmackay - 01-12-2019 09:45 PM
thanks; I've added a comment to that thread.
RE: logₓy - Benjer - 01-12-2019 10:42 PM
I was having the opposite problem the other day trying to (somewhat quickly) take the log_10 of some number on a Casio fx-991EX, but the button I was using required an argument for the base and I thought it strange there'd be a button for that but not one for log_10. I did ultimately find it as a shifted function on the (-) key. At the time I thought it interesting that logₓy had its own button but log_10 didn't.
RE: logₓy - Valentin Albillo - 01-12-2019 10:49 PM
.
Hi,
(01-12-2019 09:09 PM)cdmackay Wrote: I had cause to work out log₂ of a number today, and was vaguely surprised that I couldn't find it on my calculators, not even as a function, let alone on a key. Nor the more general logₓy.
The HP-71B has several log functions (some in the mainframe and some in various ROMs), including LOG2(X) which admittedly is very handy for all sort of programming tasks.
I also think that the HP-75 had a general Log to any base, not sure if in the mainframa or perhaps in some ROM or other.
V.
RE: logₓy - cdmackay - 01-13-2019 12:01 AM
thanks both,
(01-12-2019 10:42 PM)Benjer Wrote: I was having the opposite problem the other day trying to (somewhat quickly) take the log_10 of some number on a Casio fx-991EX, but the button I was using required an argument for the base and I thought it strange there'd be a button for that but not one for log_10. I did ultimately find it as a shifted function on the (-) key. At the time I thought it interesting that logₓy had its own button but log_10 didn't.
yup, it's not even a shifted fn there, but the main key fn.
(01-12-2019 10:49 PM)Valentin Albillo Wrote: The HP-71B has several log functions (some in the mainframe and some in various ROMs), including LOG2(X) which admittedly is very handy for all sort of programming tasks.
I also think that the HP-75 had a general Log to any base, not sure if in the mainframa or perhaps in some ROM or other.
I'll add one of those to my wish-list
RE: logₓy - Gerson W. Barbosa - 01-13-2019 12:40 AM
(01-12-2019 09:09 PM)cdmackay Wrote: It's trivial to write my own fn for e.g LOGy(x) (e.g. LOG SWAP LOG ÷), but am I missing something?
LOGx(y) sounds more natural to me:
« LN XROOT LN »
Shorter, but probably slower.
RE: logₓy - rprosperi - 01-13-2019 01:29 AM
(01-12-2019 10:49 PM)Valentin Albillo Wrote: I also think that the HP-75 had a general Log to any base, not sure if in the mainframa or perhaps in some ROM or other.
The HP-75/71 mainframes include:
LOG(X) Base e Log of X
LOG10(X) Base 10 Log of X; 71B can also use LGT(X)
The HP-75/71 MATH ROMs include:
LOG2(X) Base 2 Log of X
LOGA(X,N) Base N Log of X (75 Only)
The 71B also includes LOGP1(X) which is the value of Ln(1+x)
So, pretty complete.
RE: logₓy - Valentin Albillo - 01-13-2019 02:13 AM
rprosperi Wrote:The HP-75/71 mainframes include:
LOG(X) Base e Log of X
LOG10(X) Base 10 Log of X; 71B can also use LGT(X)
The HP-71B also has LN(X) as an alternate spelling.
Quote:The 71B also includes LOGP1(X) which is the value of Ln(1+x)
So, pretty complete.
Yes, in the HP-71B you have in all six log possibilities, namely LN, LOG, LOG10, LOG2, LOGP1, LGT and if you fancy log to any base you simply define:
10 DEF FNL(X,N)=LN(X)/LN(N)
and then you can use FNL(X,N) as part of any expression in a program, from the command line or in (urg!) CALC mode. Also, creating a new assembly-language keyword LOGA(X,N) in a LEX file is utterly trivial and would take just a few bytes.
V.
.
RE: logₓy - cdmackay - 01-13-2019 03:19 AM
(01-13-2019 12:40 AM)Gerson W. Barbosa Wrote:(01-12-2019 09:09 PM)cdmackay Wrote: It's trivial to write my own fn for e.g LOGy(x) (e.g. LOG SWAP LOG ÷), but am I missing something?
LOGx(y) sounds more natural to me:
« LN XROOT LN »
Shorter, but probably slower.
nice. I think I'd just have put in an extra SWAP, but yours is more elegant.
RE: logₓy - Dieter - 01-13-2019 08:47 AM
(01-13-2019 12:40 AM)Gerson W. Barbosa Wrote: LOGx(y) sounds more natural to me:
Yes, and I'm glad it is defined this way on the WP34s.
(01-13-2019 12:40 AM)Gerson W. Barbosa Wrote: « LN XROOT LN »
That's a nice one. And it also works in RPN, e.g. on the 35s.
Dieter
RE: logₓy - pier4r - 01-13-2019 09:11 AM
(01-13-2019 01:29 AM)rprosperi Wrote: The HP-75/71 mainframes include:
why is the 75/71 a mainframe? were those not pocket computers?
edit: ah, maybe you mean the basic library without expansion cards.
RE: logₓy - grsbanks - 01-13-2019 09:49 AM
(01-13-2019 09:11 AM)pier4r Wrote: why is the 75/71 a mainframe? were those not pocket computers?
Nobody is saying that they are mainframes. They have mainframes.
(01-13-2019 09:11 AM)pier4r Wrote: edit: a maybe you mean the basic library without expansion cards.
Correct
RE: logₓy - StephenG1CMZ - 01-13-2019 09:58 AM
A pocket computer has a mainframe?
Like Dr Who's Tardis, I guess - it's bigger on the inside.
It doesn't help that the forums on this site combine calculators and computers, so it's not immediately obvious unless you remember all the model numbers.
RE:logᵧx - Thomas Klemm - 01-13-2019 10:28 AM
(01-13-2019 12:40 AM)Gerson W. Barbosa Wrote: LOGx(y) sounds more natural to me:
We write \(\log_b(x)\) and Mathematica uses:
Quote:Log[b,z]
gives the logarithm to base b.
Thus my intuition is to use: logy(x)
Exactly as you suggested.
(01-13-2019 08:47 AM)Dieter Wrote: Yes, and I'm glad it is defined this way on the WP34s.
No, it's sad it is defined this way on the WP-34s.
Cheers
Thomas
RE: logₓy - Paul Dale - 01-13-2019 11:07 AM
All of the programming languages I used that have log to a specified base, put the base second. I.e. log(x, b).
The 34S did originally calculate logxy, but we changed the arguments around. I have a vague memory that this was to be consistent with yx, but I could be wrong.
Pauli
RE: logₓy - Dieter - 01-13-2019 12:56 PM
(01-13-2019 11:07 AM)Paul Dale Wrote: All of the programming languages I used that have log to a specified base, put the base second. I.e. log(x, b).
The 34S did originally calculate logxy, but we changed the arguments around. I have a vague memory that this was to be consistent with yx, but I could be wrong.
?!? – all 34s versions I ever used calculate logxy. That's also what is shown on the emulator skins.
I remember well the discussion about the argument order. My point is that you usually have a number in X and then you want to calculate the base-x-log of it. For a base-5-log you now simply enter 5 [logxy]. Just as you do it with powers: 5 [yx].
5 [ENTER] 3 [yx] =>125
5 [logxy] => 3
So this is similar to he mentioned log(x, b) function in the programming languages: enter x first, then the base. It's only that in RPN the x-value happens to end up in Y and the base b in X. ;-)
Dieter
RE: logₓy - cdmackay - 01-13-2019 07:40 PM
I apologise to those who prefer the other ordering/labelling
I don't think I gave it much thought, but my naive thinking involved seeing e.g. log₂ as the function, and I normally use x to denote the input of f(), leaving y as the base.
but I quite see the alternative, especially when you consider it as a function with two arguments, which of course it is.
thanks!
PS and I would normally write x-to-the-y, but it's often y-to-the-x on calculators.
RE: logₓy - Ángel Martin - 01-14-2019 03:57 PM
(01-13-2019 11:07 AM)Paul Dale Wrote: All of the programming languages I used that have log to a specified base, put the base second. I.e. log(x, b).
The 34S did originally calculate logxy, but we changed the arguments around. I have a vague memory that this was to be consistent with yx, but I could be wrong.
FWIW, and adding insult to injury, the SandMath has LOGYX where Y denotes the base and X the argument - blame it to the reverse part of RPN ;-)
RE: logₓy - cdmackay - 01-15-2019 06:07 PM
In the interests of fairness, I'm pleased to note that the Prime has both a key for logb (the 'C' key's collection of fill-in examples), and a LOG(x, b) function [CAS logb(x, b)].