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**ganesh****Administrator**- Registered: 2005-06-28
- Posts: 24,040

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???

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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

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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**ganesh****Administrator**- Registered: 2005-06-28
- Posts: 24,040

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

Any precise answer?

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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

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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**ganesh****Administrator**- Registered: 2005-06-28
- Posts: 24,040

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

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,684

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

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

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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**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,684

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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**ganesh****Administrator**- Registered: 2005-06-28
- Posts: 24,040

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

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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

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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**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,684

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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**ganesh****Administrator**- Registered: 2005-06-28
- Posts: 24,040

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.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,684

SNAP! I think we both composed our answers separately.

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**ganesh****Administrator**- Registered: 2005-06-28
- Posts: 24,040

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

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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