Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫  π  -¹ ² ³ °

You are not logged in.

## #176 2013-02-10 02:05:37

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,808
Website

### Re: A few questions

bobbym wrote:

Hi;

You can also get quite close using:

$\large \bold{ 5^{44}= \frac{10^{44}}{\left ( 2^{10} \right )^4 \cdot 2^4}}$

Hi bobbym,
What should I be doing after getting this form?

Hi stefy,
How? If I could have approximated the logarithm of 5^44, then there would have been no problem at all. Can you do it?

Last edited by Agnishom (2013-02-10 02:07:04)

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

Offline

## #177 2013-02-10 02:18:08

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: A few questions

10^44 is a 45 digit number.

2^10 ≈ 1000 = 10^3

(10^3)^4 = 10^12

10^44 / (10^12 * 2^4) = 10^32 / 2^4

Now 2^4 = 1.6 *10

10^32 / ( 1.6 * 10) = 10^31 / 1.6 ≈ 10^30.

10^30 is a 31 digit number. But this is only an approximation.

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Offline

## #178 2013-02-10 02:23:52

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,808
Website

### Re: A few questions

Yes, yes, I get it

Well, what had stefy been talkiing about?

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

Offline

## #179 2013-02-10 02:28:35

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: A few questions

You can use Taylor's series to get log(5), but it will require a little bit of calculus.

If you want to see how...

Last edited by bobbym (2013-02-10 03:15:30)

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Offline

## #180 2013-02-11 01:24:08

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,808
Website

### Re: A few questions

Indeed I want to see,

My problem is that I am not acquainted enough with calculus

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

Offline

## #181 2013-02-11 01:26:39

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: A few questions

You are a little young for your school system to have taught you it. They prefer a gradual introduction to it.

I am using log(x) to denote the common logarithm and ln(x) as the natural log.

You start with the Mclaurin series

$\small \inline \dpi{120} \bg_green \fn_cs \ln\left (\frac{1+x}{1-x} \right )=2 x+\frac{2 x^3}{3}+\frac{2 x^5}{5}+\frac{2 x^7}{7}+...+$

If we substitute x = 2 / 3 in the we get:

$\small \inline \dpi{120} \bg_green \fn_cs \ln\left (\frac{1+\frac{2}{3}}{1-\frac{2}{3}} \right )= \ln(5)\approx \frac{2\ 2}{3}+\frac{2}{3} \left(\frac{2}{3}\right)^3+\frac{2}{5} \left(\frac{2}{3}\right)^5+\frac{2}{7} \left(\frac{2}{3}\right)^7 = 1.600261284211901$

So ln(5) ≈ 1.600261284211901

But we needed log(5) not ln(5)! How do we get it?

We use this relationship

$\small \inline \dpi{120} \bg_green \fn_cs \log(x)=\frac{\ln(x))}{\ln(10) }$

$\small \inline \dpi{120} \bg_green \fn_cs \log(5)=\frac{\ln(5))}{\ln(10) }$

$\small \inline \dpi{120} \bg_green \fn_cs \log(5)=\frac{\ln(5))}{\ln(2) + \ln(5)}$

$\small \inline \dpi{120} \bg_green \fn_cs \log(5) \approx \frac{1.60026}{0.693\, +1.60026} \approx 0.698970004$

which is quite close to the true value.

Last edited by bobbym (2013-02-11 02:37:12)

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Offline

## #182 2013-02-11 01:54:28

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,808
Website

### Re: A few questions

Let me try it out

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

Offline

## #183 2013-02-11 02:03:23

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,037

### Re: A few questions

Hi bobbym

$\frac{\ln{\left (1+\frac{2}{3} \right )}}{1-\frac{2}{3}}\neq \ln{5}$

Here lies the reader who will never open this book. He is forever dead.
Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

Offline

## #184 2013-02-11 02:07:24

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: A few questions

Please hold on the latex maker is not holding up, I am aware of that and am editing the original post.

All done!

Last edited by bobbym (2013-02-11 02:27:57)

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Offline

## #185 2013-03-14 04:32:52

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,808
Website

### Re: A few questions

Please help me with the problem attached

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

Offline

## #186 2013-03-14 05:07:38

bob bundy
Administrator
Registered: 2010-06-20
Posts: 8,019

### Re: A few questions

hi Agnishom,

I'm not getting this yet.  I've drawn a line L .  Now it says 'on a straight line l' so I assumed that the circles had their centres on the line, and that each circle touches the ones on either side of it.  That covers the 'externally tangential to circle(n-1) and circle(n+1) but apparently also tangential to L itself.  How does that happen?  And I haven't even got to the second sentence yet.

Bob

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

Offline

## #187 2013-03-14 08:05:57

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,037

### Re: A few questions

I am getting 1/2.

Here lies the reader who will never open this book. He is forever dead.
Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

Offline

## #188 2013-03-14 10:42:50

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: A few questions

Hi Agnishom;

bobbym wrote:

A picture is worth a thousand words.

For people like me who are geometrically challenged this problem is a nightmare. So far I have come up with 10^16 different possible drawings that to me fit those constraints.

Now I am busy looking up externally tangent, internally tangent, tangerine tangent... in the hopes of what externally tangent to the line means. Intersects at one point?

I see that bob has got his circles with their centers on the line, I have lifted my circles and it was hard to do, after all there are an infinite amount of them, to roll on the line. That takes care of externally tangent. Now this second bunch of circles, where do they go?

John McCarthy wrote:

As the Chinese say, 1001 words is worth more than a picture.

Maybe I shouldn't need the diagram...

Last edited by bobbym (2013-03-14 19:08:18)

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Offline

## #189 2013-03-14 13:59:39

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,808
Website

### Re: A few questions

Bob, if you want I can give a diagram

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

Offline

## #190 2013-03-14 14:12:12

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,808
Website

### Re: A few questions

This is the only diagram I can imagine.

A rough sketch though...

1001 Words ≈ 7 KB
1 picture > 100 KB

Obviously, a picture is worth more....

Last edited by Agnishom (2013-03-14 14:14:14)

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

Offline

## #191 2013-03-14 14:45:43

Nehushtan
Member
Registered: 2013-03-09
Posts: 894
Website

### Re: A few questions

Agnishom wrote:

Please help me with the problem attached

This is what I got.

Let
be the centre of
and
the point of contact of
with
. Let
be the centre of
and
the point of contact of
with
.

Let

be the point on
such that
is a rectangle. Applying Pythagorass theorem to
gives
.

Let

be the point on
such that
is a rectangle. Applying Pythagorass theorem to
gives
.

Let

be the point on
such that
is a rectangle. Applying Pythagorass theorem to
gives
.

Then

Hence:

[align=center]

[/align]

Last edited by Nehushtan (2013-03-14 14:53:34)

Blog
208 books currently added on Goodreads

Offline

## #192 2013-03-14 18:19:41

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: A few questions

Hi Agnishom;

Thanks for the drawing.

Last edited by bobbym (2013-03-14 21:19:25)

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Offline

## #193 2013-03-14 19:18:18

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,808
Website

### Re: A few questions

Thanks Nehushtan
I shall ask you if I have any doubts

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

Offline

## #194 2013-03-15 13:54:42

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,808
Website

### Re: A few questions

Please upload a diagram, I really do not understand from "Applying Pythagoras Theorem..."

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

Offline

## #195 2013-03-16 04:09:30

Nehushtan
Member
Registered: 2013-03-09
Posts: 894
Website

### Re: A few questions

Here you go.

Blog
208 books currently added on Goodreads

Offline

## #196 2013-03-16 16:06:15

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,808
Website

### Re: A few questions

Thank you

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

Offline

## Board footer

Powered by FluxBB