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#1 2012-12-04 09:29:25

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

Solve the logorithmic equation

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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#2 2012-12-04 10:32:01

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

Re: Solve the logorithmic equation

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 smile


“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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#3 2012-12-04 13:24:13

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,231

Re: Solve the logorithmic equation

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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#4 2012-12-04 13:54:48

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

Re: Solve the logorithmic equation

It should be

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#5 2012-12-04 14:38:49

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,231

Re: Solve the logorithmic equation

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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#6 2012-12-04 15:35:13

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

Re: Solve the logorithmic equation

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)!  smile


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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#7 2012-12-05 05:19:26

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

Re: Solve the logorithmic equation

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

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#8 2012-12-05 08:18:50

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,231

Re: Solve the logorithmic equation

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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#9 2012-12-05 08:26:29

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

Re: Solve the logorithmic equation

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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#10 2012-12-05 09:16:48

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,231

Re: Solve the logorithmic equation

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


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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#11 2012-12-05 09:34:20

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

Re: Solve the logorithmic equation

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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#12 2012-12-05 09:46:03

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,231

Re: Solve the logorithmic equation

Yes, writing the Principia Mathematica nearly killed me.


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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#13 2012-12-05 11:38:00

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

Re: Solve the logorithmic equation

It nearly killed me reading it.

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#14 2012-12-05 12:40:55

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,231

Re: Solve the logorithmic equation

Hi;

For that I apologize.


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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#15 2012-12-05 21:56:07

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

Re: Solve the logorithmic equation

So, you are the genius behind Russell?


“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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#16 2012-12-05 22:00:24

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,231

Re: Solve the logorithmic equation

No, I am doing as you instructed.


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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#17 2012-12-05 22:04:26

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

Re: Solve the logorithmic equation

And what is it that I instructed?


“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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#18 2012-12-05 22:07:13

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,231

Re: Solve the logorithmic equation

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.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#19 2012-12-05 22:09:11

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

Re: Solve the logorithmic equation

And did you know I never said that?


“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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#20 2012-12-05 22:10:37

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,231

Re: Solve the logorithmic equation

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.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#21 2012-12-06 21:56:49

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

Re: Solve the logorithmic equation

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.

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

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#22 2012-12-06 22:05:37

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,231

Re: Solve the logorithmic equation

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.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#23 2012-12-06 22:14:32

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

Re: Solve the logorithmic equation

Yup!


“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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#24 2012-12-06 22:23:44

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,231

Re: Solve the logorithmic equation

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.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#25 2012-12-06 22:25:35

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

Re: Solve the logorithmic equation

Which problem is that?


“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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