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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: Harlan's World
- Registered: 2011-05-23
- Posts: 16,018

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

The knowledge of some things as a function of age is a delta function.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 106,389

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.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**scientia****Member**- Registered: 2009-11-13
- Posts: 224

It should be

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 106,389

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.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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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: 106,389

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.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,018

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

The knowledge of some things as a function of age is a delta function.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 106,389

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

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,018

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

The knowledge of some things as a function of age is a delta function.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 106,389

Yes, writing the Principia Mathematica nearly killed me.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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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: 106,389

Hi;

For that I apologize.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,018

So, you are the genius behind Russell?

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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 106,389

No, I am doing as you instructed.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,018

And what is it that I instructed?

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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 106,389

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

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,018

And did you know I never said that?

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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 106,389

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

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,018

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

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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 106,389

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

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,018

Yup!

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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 106,389

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

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,018

Which problem is that?

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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