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## #1 2013-02-10 03:53:39

debjit625
Member
Registered: 2012-07-23
Posts: 101

### Logarithm problem

May be its simple but I can't solve it...
Show that : log2(2log(base 4) 5 + 1) = 1
$log_{10}2(2log_{4}5+1) = 1$

Thanks

Last edited by debjit625 (2013-02-10 20:16:22)

Debjit Roy
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## #2 2013-02-10 03:57:42

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

### Re: Logarithm problem

Hi debjit625

The LaTeX on this forum isn't functioning at the moment so here is the picture with what you presumably want to show:
$\log_{10}{2}\cdot(2\log_{4}{5}+1)=1$

Do you know what $\frac{1}{\log_{a}{b}}$ is equal to?

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.

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## #3 2013-02-10 04:08:23

debjit625
Member
Registered: 2012-07-23
Posts: 101

### Re: Logarithm problem

Ok I was having problem with  Latex.... and yes thats write.

1/log(base a)b = log(base b)a ,is that what you wanted to know

Thanks

Debjit Roy
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The essence of mathematics lies in its freedom - Georg Cantor

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## #4 2013-02-10 04:21:43

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

### Re: Logarithm problem

Hi debjit625

Yes, that is the one. Do you see how you can use it here?

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.

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## #5 2013-02-10 04:33:14

debjit625
Member
Registered: 2012-07-23
Posts: 101

### Re: Logarithm problem

No,not sure.
I can use that inside the bracket to solve log(base 4) 2 to log/(base2)4 ....

Thanks

Debjit Roy
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The essence of mathematics lies in its freedom - Georg Cantor

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## #6 2013-02-10 04:50:55

debjit625
Member
Registered: 2012-07-23
Posts: 101

### Re: Logarithm problem

I am not sure how to do it ...still confused

Debjit Roy
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The essence of mathematics lies in its freedom - Georg Cantor

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## #7 2013-02-10 05:06:46

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

### Re: Logarithm problem

Hi

See the hidden text from my last post.

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.

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## #8 2013-02-10 18:29:38

debjit625
Member
Registered: 2012-07-23
Posts: 101

### Re: Logarithm problem

Sorry I cant understand...
dividing both the sides by "log (base 10) 2" will give us
$2log_45+1 = log_210$
2log(base 4)5 + 1 = log (base 2) 10

Thanks

Last edited by debjit625 (2013-02-10 20:14:15)

Debjit Roy
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The essence of mathematics lies in its freedom - Georg Cantor

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## #9 2013-02-10 19:01:22

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

### Re: Logarithm problem

That is correct. Can you proceed from here or do you need the next step?

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.

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## #10 2013-02-10 19:44:31

debjit625
Member
Registered: 2012-07-23
Posts: 101

### Re: Logarithm problem

I need the next step ...
I am not sure how to prove LHS is equal to 1,shouldn't we only work with LHS and prove/show it is 1?

Thanks

Debjit Roy
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The essence of mathematics lies in its freedom - Georg Cantor

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## #11 2013-02-10 23:12:11

bob bundy
Registered: 2010-06-20
Posts: 8,065

### Re: Logarithm problem

hi debjit625

I'd get everything in the same log base.  As it is easy to get log base 4 into log base 2 that's the next step:

log(base4)5 = log(base2)5/log(base2)4 = (log(base2)5)/2

so your expression (from post 8) becomes (all logs now in base 2):

(2log5)/2 + 1 = (2log5)/2 + log2

Should be easy to finish from there.

Bob

Last edited by bob bundy (2013-02-10 23:15:03)

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

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## #12 2013-02-10 23:54:16

debjit625
Member
Registered: 2012-07-23
Posts: 101

### Re: Logarithm problem

Well that solved the problem ,but still I have questions...
I understood that you used change base formula on LHS to change the base of
$log_45=\frac{log_25}{log_24}=\frac{log_25}{2}$

bob bundy wrote:

hi debjit625
so your expression (from post 8) becomes (all logs now in base 2):
(2log5)/2 + 1 = (2log5)/2 + log2
Bob

But what I didnt understood is that how you got it on RHS
$2\frac{log_25}{2}$

As per me its like this
$log_{10}2(2log_45+1) = 1$

$2log_45 + 1 = log_210$

$2\frac{log_25}{2} + 1 = log_2(2*5)$

$log_25 + 1 = log_22 + log_25$

Thanks everybody it seems I have to learn a lot ,off course from you guys...

Last edited by debjit625 (2013-02-11 00:22:09)

Debjit Roy
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The essence of mathematics lies in its freedom - Georg Cantor

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## #13 2013-02-10 23:55:39

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

### Re: Logarithm problem

Hi Roy

You need to remove all spaces from those links.

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

## #14 2013-02-11 01:11:13

bob bundy
Registered: 2010-06-20
Posts: 8,065

### Re: Logarithm problem

hi debjit625

What you have done is equivalent to my version.

Strictly, you should have LHS = ... = ... = ... = RHS.

But you have all the elements to re-write it like that now.

Hints:  1 = log(base n) n      for all n                    and       log(base a)b x log(base b) a = 1 for all a and b

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

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