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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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Sorry but I can not make any sense out of the second one. There are just too many ways to group that. Please group it.

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**EbenezerSon****Member**- Registered: 2013-07-04
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But that was how it exists in the book and I tried to solve.

Think the following is how it came by its answder.

Logy^2-log2x=log2y-log2x

(y^2/2x)= 2x(2y-2x).

y^2= 4xy-4x^2

y^2= 4xy-4x^2

y^-4xy+4x^2=0 I think could be factorised,

My question is, as there became a negative sign between log2y-log2x I think should be log(2y/2x). As the law says logx-logy=(x/y).

But why only the law affected the left hand equation only I mean (y^2/2x) and not the right hand as well?

Please assist.

*Last edited by EbenezerSon (2013-08-03 10:00:14)*

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**EbenezerSon****Member**- Registered: 2013-07-04
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I know the book is right, but I can not figure out as to why it applied the law of division on the left equation only. I could see the right equation also has a negative sign between it and I think should be

lo2y/log2x so that it would also have a division sign as the left equation has. Then from there one can work it down.

Bobbym, why do you think the division sign was denied on the right hand equation only?

Or is only left hand equations that must assume it? And not right hand equations?

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**anonimnystefy****Real Member**- From: The Foundation
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Notice that your right hand side isn't the same as in the original problem from post #194.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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That book has lots of mistakes in it:

Last but not the least

log81/log3^1.

the book has -4 at its back as the answer.

I am getting 4 not -4.

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**zetafunc.****Guest**

Which textbook are these questions from?

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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I have not asked him that yet.

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**EbenezerSon****Member**- Registered: 2013-07-04
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Anonynmstify, if I am getting you right I think youre right, but then when you work it down you would arrive on the division sign, watch:

2logy-log2x=log2(y-x).

logy^2 - log2x = log2y-2x. Now, there come a negative sign at the right equation.

I am thinking that, since there is a negative sign in both the right and the left equation, both sides must have that division sign respectively. But to my suprise only the left equation had the division sign. Still I am not clear.

Bobym let me know why +4.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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Last but not the least

log81/log3^1.

the book has -4 at its back as the answer.

Now just cancel the log(3) on the top and bottom.

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**EbenezerSon****Member**- Registered: 2013-07-04
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Bobym, please could you produce the methods here, if the log3^1 were to be log1/3. What would be the answer?

Thanks.

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**bobbym****Administrator**- From: Bumpkinland
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The method is in post #209, I showed the three steps.

If the denominator was 1 / 3 instead of 3 then the answer would be -4.

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**EbenezerSon****Member**- Registered: 2013-07-04
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Thanks, Bobbym!

God bless.

1/3logp=1. Find the value of p.

Bobbym, how would one do this? I have tried and my answer was not the same as what the book has.

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**anonimnystefy****Real Member**- From: The Foundation
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p=1000.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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1/3logp=1

Times both sides by 3

log(p) = 3

Take 10^ of both sides.

p = 10^3 = 1000

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**EbenezerSon****Member**- Registered: 2013-07-04
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See, I am taking aback as to why the answer is 1000.

Because I have learnt that any number raised to power either 1/3, 1/2, 1/4. is demanding the third the square and the fourth root of that number. I see it that if the answer is 1000 in the above problem then the question should have been:

3logp=1. so that it would be,

log p^3=log10. taking antilog.

p^3 = 10

p =10^3.

p=1000

Please, anyone correct me if I am wrong.

Thanks.

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**EbenezerSon****Member**- Registered: 2013-07-04
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I mean

1/3logp=1

logp^1/3=10

p =10^1/3

third root is required.

p=2.15.

I am not saying anyone is wrong but this suprise me, c'os I have applied what I am talking about for long.

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**bobbym****Administrator**- From: Bumpkinland
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Line 3 is incorrect.

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**EbenezerSon****Member**- Registered: 2013-07-04
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Okay, then is the following correct?

For instance.

y^1/3=a. would be a^

3

y^3 = a. square root of a would then be taken.

Is the above right?

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**bobbym****Administrator**- From: Bumpkinland
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First one is okay.

y^3 = a. square root of a would then be taken.

You mean cube root.

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**EbenezerSon****Member**- Registered: 2013-07-04
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yes, yes, cube root instead.

But are they all right in that manner?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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Yes, they are correct.

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**anonimnystefy****Real Member**- From: The Foundation
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Have you sorted out the x and y problem?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,485

What x and y problem?

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**anonimnystefy****Real Member**- From: The Foundation
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EbenezerSon wrote:

If 2logy-log2x=2log(y-x), express y in terms of x. I had (y-x)(y-2x^2). The book has y^-4xy+4^2x=0.

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**EbenezerSon****Member**- Registered: 2013-07-04
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I have solved it but this way:

2logy-log2x = log2(y-x).

log(y^2/2x) = log2y-log2x. this is where I think the divison must apply to the right hand ones.

(y/2x) =(2y-2x) Taking antilogs

(y^2/2x) = 2x(2y-2x)

y^2 = 4xy-4x^2

y^2-4xy+4x^2 = 0

y^2-2xy-2xy+4x^2=0

y(y-2x)-2x(y-2x)=0

(y-2x)(y-2x)=0

(y-2x)^2.

My question is why not log2y-2x is not made to be log(2y/2x), since it has that negative sign? **In order to go by the law**.

Please clear my doubt.

Thanks much.

*Last edited by EbenezerSon (2013-08-04 10:14:08)*

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