All Answers 358155 Answers

Definition:

$$x = log_b(a) \Leftrightarrow b^x = a \,\,\,\, (for \,\, a,b >0 \,\, and \,\, b<>1)$$

Formula to convert logarithm base g to base b:

$$log_b(x) = log_b(g) * log_g( x )$$

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4^300 = number "a"  is a really large number, but we don't care what the actual number is, instead we want to know how many digits the number has:

4^300 = a 

 300 = log4( a  )

and:

 log10( a) = log10( 4 ) * log4( a ) = log10( 4 ) * 300

 log10( a) = log10( 4 ) * 300

log10( a ) = 180.61799739838872 ( so about 180 digits)

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3^400 = b

 400 = log3( b  )

and:

 log10( b) = log10( 3 ) * log3( b ) = log10( 3 ) * 400

 log10( b) = log10( 3 ) * 400

log10( b ) = 190.848501887864976 ( so about 190 digits)

CONGRATULATIONS CHRIS!

YOU HAVE THE POWER!!!

I can only do that with my "normal" answers........LOL!!!

Okay Chris.

I thought you might be able to argue different cases to get different answers and hence end up with undefined.

Thank you.

It's right there in my eighth "sentence".......

"Thus,   ∞ - ∞ = ∞"..........

This is one way you can think of it.

If it were -40 degrees centigrade it would be very cold.  If it were +40 degrees centigrade it would be very hot

so

negative numbers are cold numbers and positive numbers are hot numbers.

0- -2 is 0degrees take away some cold.  if you take away some cold air it must get hotter! so - - = +

0- -2 = 0+2 = 2

0 - (-2)

0 + 2

2

Subtracting by a negative is the same as adding a regular number, the subtract sign and negative cancel each other out.

You know Chris, you never really did give an answer.  

@Anon: As I said before, this si my least favorite thing about math, and that my understanding is rudimentary at best. I knew there were flaws, but I also knew the general answer. That is why I asked for clarification.

Thanks Chris and David and thank you Anana for you good manners.

If you give the answers you like a thumbs up you can give them lots of points!  You have the POWER!

There is a post on here titled

A Method of Statistical Inference on Two-dimensional Object Ratios

It broaches infinities – it is a brilliant peace of work.

This is who David is referring to.

101 thanks

On first blush, we might consider the answer to be "0.'

But, it's not.....

Consider the set of integers on the number line. You will agree - I hope - that this set is infinite. Now, consider the set of even integers on the number line. Again, we'll consider this set to be infinite, too.

So, subtracting the second "infinity" from the first "infinity," we end up with another infinite set - the set of all odd integers !!

Thus,   ∞ - ∞ = ∞

Also, notice another odd property......I've divided one set in half and gotten another infinite set. Thus....

∞ / 2  = ∞

One more interesting idea, and then I'll shut up.  Which "infinity" is "greater?"  The set of all positive integers, or the set of all positive even integers??

Note, that I can "count" each positive even integer.....For example, 2 is the first one, 4 is the second one, etc. Thus, I can put each positive even integer into a one-to-one correspondence with a "counting" number. And since I can do so, then the set of positive even integers must be just as large as the set of all the positive integers !!!

I would say it is "aleph null" or undefined, unless the infinities are explicitly defined as countable, but I'll ask Georg Cantor.

Well, it is probably zero but (It is not)  someone else should give their thoughts on the matter.

DavidQD you are on the forum - what do you think?

lol idk idc

It is not proper for a lowly servant to contradict the lady of the land !!

My husband, King Arthur, is eager for another head to hang in the royal court.

It will serve as a deterent for other potentially disrespectful lowly servants!

Lady Guinevere.

@@ End of Day Wrap - Sat 10/5/14   Sydney, Australia Time 23:00 

Hi everyone,

It was a standard quiet Friday/Saturday.  But, as always, there were some good answers.  These were given by CPhill, Alan, GoldenLeaf and Capricious unicorn.  Thank you all.

**If people are going to give an answer that comes from a calculator I would ask that the site calc by means of the [Math (Input=Result)] button is used.  It makes it much easier for people to check that the calculation is in fact correct. Plus, once you get used to it is is easier than reaching for a different calculator.

These posts maybe of some interest to some of you.

This one has not yet been answered

OEIS - Online Encylopedia of Integer Sequences

You see yourself as court physician? Do you treat anaemia with leaches?

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Sometimes with leaches, other times I use a barber’s razor. It’s effective for many things, except Dense Fog, M’ Lady.

In many cultures a 13 year old is considered a man ...

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Perhaps, M’ Lady. However in this culture, a man must shave or be shaved. The inscription do sayth accordingly.

Yes....you are correct, Melody.......I should have said it is undefined everywhere except for my answer.......

In many cultures a 13 year old is considered a man.  

Thus the man may indeed be prepubescent.

Perhaps GoldenLeaf may consider such a 'man' a young boy.  But in this instance it is not GoldenLeaf's interpretation but the attitiude of the society that the 13year old lives in that is of consequence.  Hence, GoldenLeaf's solution to the dilemma is perfectly valid!

hi Chris,

Isn't this where it IS defined?  The question asks for where it is not defined.