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**debjit625****Member**- Registered: 2012-07-23
- Posts: 89

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: The Foundation
- Registered: 2011-05-23
- Posts: 14,836

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?

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Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

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**debjit625****Member**- Registered: 2012-07-23
- Posts: 89

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: The Foundation
- Registered: 2011-05-23
- Posts: 14,836

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

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**debjit625****Member**- Registered: 2012-07-23
- Posts: 89

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: 89

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: The Foundation
- Registered: 2011-05-23
- Posts: 14,836

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

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**debjit625****Member**- Registered: 2012-07-23
- Posts: 89

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: The Foundation
- Registered: 2011-05-23
- Posts: 14,836

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.

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**debjit625****Member**- Registered: 2012-07-23
- Posts: 89

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****Moderator**- Registered: 2010-06-20
- Posts: 6,114

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)*

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: 89

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: The Foundation
- Registered: 2011-05-23
- Posts: 14,836

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.

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,114

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

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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