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**gbrad88****Member**- Registered: 2012-12-03
- Posts: 16

Solve the logorithmic equation

log(8) x + log(8) (x-63) = 2

The correct answer is listed as 64.

I'm trying to learn and understand the correct way of coming down to that answer with out using a calculator. Thanks.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,544

Have you tried raising 8 to the power of lhs and rhs?

Just in case you don't kmow:

LHS means "left hand side"

RHS means "right hand side"

Better safe than sorry

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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,192

Hi;

The correct answer is listed as 64.

I am not getting that. Is this the correct equation?

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**scientia****Member**- Registered: 2009-11-13
- Posts: 222

It should be

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,192

Hi;

Thanks scientia!

As the man said, "Notation, notation, notation!"

"Our ships must all sail in the same direction."-Don Lucchesi

raise up everything to the power of 8.

Plug back in to the original equation to see that 64 is a root.

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**noelevans****Member**- Registered: 2012-07-20
- Posts: 236

Hi!

Or using the laws of logarithms the LHS = log [x(x-63)] so log [x^2-63x] = 2.

8 8

Converting to exponential notation (or making both sides exponents for 8) we have

2

8 = x^2 - 63x so that x^2 - 63x - 64 = 0. And upon factoring the LHS: (x-64)(x+1) = 0.

Hence x=64 or x=-1. We can eliminate the -1 if we don't wish to get into complex numbers.

Converting from log notation to exponential notation and visa versa is simple:

log y = z is equivalent to

x

z

x = y

If we write the base x for both the log and the exponential on the same side (left here) then

the other two quantities ( y and z here) switch sides.

x

Other examples: log 32 = x becomes 2 = 32 (so x=5)

2

x -2

log (1/9) = x becomes 3 = 1/9 = 3 hence x=-2.

3

3

5 = 125 becomes log 125 = 3.

5

and so forth.

logarithms ARE EXPONENTS. It's just a naming device so we can tell what base they are supposed

to go on and to see what the result should be if we put in on that base.

log100

Example: 10 log100 is the exponent we must put on 10 to get 100.

2

Since 10 = 100, log100 = 2.

lnx lnx

e lnx is the exponent we must put on e to get x. Hence e = x.

log N

b

In general b = N so log N is the exponent we must put on b to get N. (b>0 and b<>1).

b

Have a great day (or night as the case may be)!

Writing "pretty" math (two dimensional) is easier to read and grasp than LaTex (one dimensional).

LaTex is like painting on many strips of paper and then stacking them to see what picture they make.

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**gbrad88****Member**- Registered: 2012-12-03
- Posts: 16

Thanks, especially bobbym, your process I followed helps a lot.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,192

Hi;

Actually that thanks should go to anonimnystefy who showed the way and scientia for figuring out what you wanted.

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,544

No, it goes to you guys.

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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,192

Okay, then I will take all the credit everywhere, for everything.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,544

Everywhere?

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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,192

Yes, writing the Principia Mathematica nearly killed me.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**gbrad88****Member**- Registered: 2012-12-03
- Posts: 16

It nearly killed me reading it.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,192

Hi;

For that I apologize.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,544

So, you are the genius behind Russell?

Here lies the reader who will never open this book. He is forever dead.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,192

No, I am doing as you instructed.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,544

And what is it that I instructed?

Here lies the reader who will never open this book. He is forever dead.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,192

To take credit for everything, everywhere. Did you know I invented aluminum foil?

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,544

And did you know I never said that?

Here lies the reader who will never open this book. He is forever dead.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,192

But you certainly tempted me to do it. Did you realize I am the discoverer of Pluto?

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,544

You do realize that I gave you credit just for this problem?

Here lies the reader who will never open this book. He is forever dead.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,192

Then I did not really discover Pluto or write the Principia Mathematica? Perhaps you will now say that I did not invent aluminum foil?

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

**Online**

**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,544

Yup!

Here lies the reader who will never open this book. He is forever dead.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,192

Okay, but I did invent the method I used on Agnishom's problem...

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,544

Which problem is that?

Here lies the reader who will never open this book. He is forever dead.

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