Re: Request for Assistance on Logs/Anti-LOGS


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Re: Request for Assistance on Logs/Anti-LOGS



> This is how I learned logarithms:
> a^b=c
> if a and c are known, and you want b, you do
> log (base a) c
> Okay, so maybe that's not strictly an inverse but you know what I mean.

Just trying to make the details precise. Fuzzy details is what eventually
gets ya in math AND life. Ya know the Mars lander that crashed and burned
this year or the Hubbel 'scope? All those guys knew what each other meant!

> It's the backwards of the more common operation.  Anybody aware of that
> definition should not have to ask how to find the antilog.  In a similar
> fashion,

They'd have to ask if they'd never heard the word "antilog", which they
probably won't in today's math books. An Altavista search for it turned up
only 932 occurrences, as opposed to the 27000+ the logarithm turned up. Of
the first 10 antilog hits, only 3 distinct web sites were listed. One of
those was in the UK, where maybe the term is still commonly used.

We DO have to be able to read the older books, and those from other
countries, too.

> sin a = b
> arcsin b = a
> Anybody aware of that definition would not have to ask how to find the
> inverse of the arcsin.  It was just an analogy, albeit a poor one.

It wasn't poor, just not precise. The above isn't so precise either IF you
are trying to define inverse FUNCTIONS as are defined in all scientific and
graphing calculators.

"IF |y|<=pi/2, then arcsin(x)=y is equivalent to sin(y)=x ".
(This has the effect of limiting the range of the arcsin so that it IS a
function. Another way to look at is that the sin function has to be made 1-1
so its inverse will be a function, and this interval is the "best" place to
limit its domain.)

Some old texts once used Arcsin to designate the FUNCTION and arcsin to
designate
the non-function, which does NOT have the "pi/2" restriction. CasE alone was
the determiner. Talk about unfriendly!

Dave Slomer
Greenhills, OH
davidslomer@geocities.com
http://www.geocities.com/CapeCanaveral/Lab/8692/

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