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#1 2005-06-30 18:56:14

ganesh
Moderator
Registered: 2005-06-28
Posts: 14,522

What went wrong?

Tell me, where I go wrong

Step (1) :-  1/4 > 1/8
Step (2) :- (1/2)^2 > (1/2)^3
Taking log on both sides
Step (3) :- 2 log (1/2) > 3 log (1/2)
Cancelling log (1/2) on both sides
Step (4) :- 2 > 3
Obviously, 2 is not greater than 3,
but I started with a correct inequation;
Where did I go wrong???


Character is who you are when no one is looking.

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#2 2005-06-30 20:07:44

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

Re: What went wrong?

Something to do with not being allowed to divide by negatives?

Last edited by mathsyperson (2005-06-30 20:30:35)


Why did the vector cross the road?
It wanted to be normal.

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#3 2005-06-30 20:23:47

ganesh
Moderator
Registered: 2005-06-28
Posts: 14,522

Re: What went wrong?

I guess you know the answer, but unable to put it in proper words...
Any precise answer?


Character is who you are when no one is looking.

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#4 2005-06-30 20:32:10

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

Re: What went wrong?

I don't know the answer at all, I'm just guessing!
That's the only difference I know between equations and inequalities, so I thought it might have something to do with that.
*Tries to edit*

Last edited by mathsyperson (2005-07-05 01:02:39)


Why did the vector cross the road?
It wanted to be normal.

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#5 2005-06-30 20:59:27

ganesh
Moderator
Registered: 2005-06-28
Posts: 14,522

Re: What went wrong?

Lets wait for more responses......I shall give the solution soon...


Character is who you are when no one is looking.

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#6 2005-06-30 21:06:38

MathsIsFun
Administrator
Registered: 2005-01-21
Posts: 7,535

Re: What went wrong?

This is a good one, ganesh.

Don't give the answer too soon, let us all have a go at it ...

(Also, some members don't try them straight away to give others a chance)


"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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#7 2005-06-30 21:13:12

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

Re: What went wrong?

MathsIsFun wrote:

(Also, some members don't try them straight away to give others a chance)

I do that on the puzzles board, but if someone puts one on the 'Help Me' board then I do it straight away as I assume that they need help.

Wait a minute... when I say assume it changes it to math!

Last edited by mathsyperson (2005-06-30 21:13:59)


Why did the vector cross the road?
It wanted to be normal.

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#8 2005-07-01 03:35:41

Roraborealis
Member
Registered: 2005-03-17
Posts: 1,594

Re: What went wrong?

OK, I'll sort it out.


School is practice for the future. Practice makes perfect. But - nobody's perfect, so why practice?

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#9 2005-07-01 10:31:21

MathsIsFun
Administrator
Registered: 2005-01-21
Posts: 7,535

Re: What went wrong?

It is the censorship mechanism - it has some general rules which sometimes catch inoffensive words.

Oh, and quite a good approach, mathsy. Also, I don't mean to hold anyone back from solving puzzles... it was just an observation of mine.


"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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#10 2005-07-04 16:29:43

ganesh
Moderator
Registered: 2005-06-28
Posts: 14,522

Re: What went wrong?

When I moved from step(2) to step(3),
I was taking logarithm of 1/2.
Logarithm of 1/2 is a negative number.
(For example, logarithm(base10) of 1/2 is -0.3010 approximately)
When an inequation is mutliplied by a negative number,
the inequality reverses direction.
Thats it!
eg. 5>2
But when this inequation is multiplied by -2,
-10<-4


Character is who you are when no one is looking.

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#11 2005-07-04 18:57:41

Roraborealis
Member
Registered: 2005-03-17
Posts: 1,594

Re: What went wrong?

What is 'log' and 'logarithm'?


School is practice for the future. Practice makes perfect. But - nobody's perfect, so why practice?

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#12 2005-07-04 20:09:28

MathsIsFun
Administrator
Registered: 2005-01-21
Posts: 7,535

Re: What went wrong?

In 10² = 100, the ² is the log (base 10) of 100.

It is whatever "power" (or "exponent") you need to use to get the base to equal the number.

Usually the base is 10 or e (2.71828...) If it is 10 people say "log" or "the base 10 logarithm", if it is "e", then people just say "ln" or "natural logarithm"

So, the base 10 log of 1000 is 3, and the base 10 logarithm of 0.1 is -1 (because 10^-1 = 0.1)

Play around with it on your calculator, and it becomes easy.


"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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#13 2005-07-04 20:11:49

ganesh
Moderator
Registered: 2005-06-28
Posts: 14,522

Re: What went wrong?

10 raised to the power 6 is 1,000,000.
We say Logarithm of 1,000,000 to the base 10 is 6.
if a^b=c
(read as a raised to the power b equals c)
then, Logarithm of c to the base a is b.
In short, we say log(to the base a)  c = b
Common logarithm uses the base 10,
Natural logarithm uses the base 'e'.
Logarithms, discovered by John Napier, makes calculations far easier.
Multiplying two numbers is simply adding their logarithms (to the same base).
For example, logarithm value (to base 10) of a few numbers are given.
log 2 = 0.30103
log 3 = 0.47712
log 7 = 0.8451
log 10 = 1
and so on.


Character is who you are when no one is looking.

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#14 2005-07-04 20:19:48

MathsIsFun
Administrator
Registered: 2005-01-21
Posts: 7,535

Re: What went wrong?

SNAP! I think we both composed our answers separately.


"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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#15 2005-07-04 20:22:27

ganesh
Moderator
Registered: 2005-06-28
Posts: 14,522

Re: What went wrong?

oh yes, we did....Maybe we started the same time, but you finished earlier.


Character is who you are when no one is looking.

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