Solve the logorithmic equation

gbrad88 · 2012-12-04 09:29:25

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.

anonimnystefy · 2012-12-04 10:32:01

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

bobbym · 2012-12-04 13:24:13

Hi;

The correct answer is listed as 64.

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

scientia · 2012-12-04 13:54:48

It should be

bobbym · 2012-12-04 14:38:49

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.

noelevans · 2012-12-04 15:35:13

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)!

gbrad88 · 2012-12-05 05:19:26

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

bobbym · 2012-12-05 08:18:50

Hi;

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

anonimnystefy · 2012-12-05 08:26:29

No, it goes to you guys.

bobbym · 2012-12-05 09:16:48

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

anonimnystefy · 2012-12-05 09:34:20

Everywhere?

bobbym · 2012-12-05 09:46:03

Yes, writing the Principia Mathematica nearly killed me.

gbrad88 · 2012-12-05 11:38:00

It nearly killed me reading it.

bobbym · 2012-12-05 12:40:55

Hi;

For that I apologize.

anonimnystefy · 2012-12-05 21:56:07

So, you are the genius behind Russell?

bobbym · 2012-12-05 22:00:24

No, I am doing as you instructed.

anonimnystefy · 2012-12-05 22:04:26

And what is it that I instructed?

bobbym · 2012-12-05 22:07:13

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

anonimnystefy · 2012-12-05 22:09:11

And did you know I never said that?

bobbym · 2012-12-05 22:10:37

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

anonimnystefy · 2012-12-06 21:56:49

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

bobbym · 2012-12-06 22:05:37

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

anonimnystefy · 2012-12-06 22:14:32

Yup!

bobbym · 2012-12-06 22:23:44

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

anonimnystefy · 2012-12-06 22:25:35

Which problem is that?

Math Is Fun Forum

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

Solve the logorithmic equation

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

Re: Solve the logorithmic equation

#3 2012-12-04 13:24:13

Re: Solve the logorithmic equation

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

Re: Solve the logorithmic equation

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

Re: Solve the logorithmic equation

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

Re: Solve the logorithmic equation

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

Re: Solve the logorithmic equation

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

Re: Solve the logorithmic equation

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

Re: Solve the logorithmic equation

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

Re: Solve the logorithmic equation

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

Re: Solve the logorithmic equation

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

Re: Solve the logorithmic equation

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

Re: Solve the logorithmic equation

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

Re: Solve the logorithmic equation

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

Re: Solve the logorithmic equation

#16 2012-12-05 22:00:24

Re: Solve the logorithmic equation

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

Re: Solve the logorithmic equation

#18 2012-12-05 22:07:13

Re: Solve the logorithmic equation

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

Re: Solve the logorithmic equation

#20 2012-12-05 22:10:37

Re: Solve the logorithmic equation

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

Re: Solve the logorithmic equation

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

Re: Solve the logorithmic equation

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

Re: Solve the logorithmic equation

#24 2012-12-06 22:23:44

Re: Solve the logorithmic equation

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

Re: Solve the logorithmic equation

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