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

May be its simple but I can't solve it...

Show that : log2(2log(base 4) 5 + 1) = 1

Thanks

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

Debjit Roy

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The essence of mathematics lies in its freedom - Georg Cantor

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

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:

Do you know what is equal to?

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

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

Hi debjit625

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

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

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

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

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The essence of mathematics lies in its freedom - Georg Cantor

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

Hi

See the hidden text from my last post.

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

Sorry I cant understand...

dividing both the sides by "log (base 10) 2" will give us

2log(base 4)5 + 1 = log (base 2) 10

Thanks

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

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The essence of mathematics lies in its freedom - Georg Cantor

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

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

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

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

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The essence of mathematics lies in its freedom - Georg Cantor

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**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,053

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

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

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

As per me its like this

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)*

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The essence of mathematics lies in its freedom - Georg Cantor

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

Hi Roy

You need to remove all spaces from those links.

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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**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,053

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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