Re: Opening

Tina Hall wrote:
Tim S <Tim@xxxxxxxxxxxxxxxxxxxxxxxx> wrote:

often log base 10 is a key
labelled "log" and log base e is a key labelled "ln".)

Got them. :) (Not that I'm able to use them.)

Well, now I've even seen them on your picture!


This follows from the fact that log(n^y) = y log(n), which is kind of
part of the definition of a logarithm.

I have no idea what that means.

OK, I don't think I'll talk about it any more, then. I was hoping a bit of explanation might be more help than just telling you what keys to press, but I guess sometimes it just doesn't work out.


If you know the 25 and the 2, you can do 25^(1/2) to get the 5, and,
generally, if n^y = x, then x^(1/y) = n. In fact, a lot of
calculators have a x^(1/n) button. In the particular case of raising
to the power 2, you can also use the square root instead to go the
other way. Sqrt(n) is just n^(1/2), but this is such a common
operation that most calculators have a special square root button
(some have a special square button as well).

Don't know if this is at all helpful ... :-(

It is. Thanks.

Why only 'generally' "if n^y=x then x^(1/y)=n"?

Actually, when I said "generally" I meant "always". Now you've made me think about it, I realise it isn't true if y = 0 (since then 1/y doesn't exist).


What exacty is done to get the y from one side of the equation to the other, still up there as it is? [*]

You raise both sides to the power 1/y or (describing the same thing a different way) you take the yth root of both sides. The yth root cancels out the yth power.


And, no need to answer if too complicated, how would it look to get the y on one side all by itself? Without that logarithm stuff? (Unless you want to explain that.)

You can't do it without the logarithm stuff ... :-(


(The whole exponential stuff is still a mystery to me. I know how to execute n^y, but to me that just looks like an abbreviation of a long calculation, the y not really being part of the n*n*n*n.... If you enter y as part of a genuine calculation, I don't know what's going on anymore. That you get y zeros if n is 10 is coincidence, not true with all the other possible numbers.

It's not a coincidence. It's because the number system we use is based on powers of 10. (We could use powers of some different number -- that's what binary and hexadecimal are about. The ancient Babylonian used powers of 60 for some technical calculations, e.g. in astronomy, which is where we get 60 seconds in a minute and 60 minutes in an hour from.)

If it is in some weird way, I'd like to know how.)

[*] What I mean is, if it were:

a / b = x

You would do (*b) to get:

a = x * b

Basically, what the logarithms do is take something about powers and roots, and turn it into something about multiplication and division. So you take

n^y = x

and you take the logarithm of both sides, and get

y * log(n) = log(x).

And then you can solve for y, by dividing both sides by log(n).

This in turn follows from the fact that logarithms are designed to turn multiplication into addition, so if we have

a * b = c

and we take the logarithm of both sides, we get

log(a) + log(b) = log(c).

So if we have

a^n

which is just

a * a * a * ... * a

(where there are n copies of a, and the dots are because couldn't be bothered to write out n copies, where n is an arbitary number :-) )

then we take the logarithm and get

log(a) + log(a) + log(a) + ... + log(a)

(where there are n copies of log(a) )

which is just

n * log(a).

Tim
Having a bad feeling this discussion is just going to get deeper and deeper ...
.

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