Math Is Fun Forum

mathlover002

Guest

natural log - finding both roots?

hi,

the question says:

ln(2x+6) + ln(8x) = 2ln(x)

here is what i did to get one root:

so x = 0 and x = -1.2...

it says i got the -1.2 right, but the x = 0 is wrong and -3.2 is the right answer...

could anyone explain how i could end up getting -3.2 as the right root?

i understand you cannot take ln of 0.

thanks!

Bob

Administrator

Registered: 2010-06-20

Posts: 10,164

Re: natural log - finding both roots?

hi

Where you have 18, I think you meant 48.

Try that.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

mathlover002

Guest

Re: natural log - finding both roots?

hi,

i cant believe i made that mistake, i am so stupid..i have no idea why i did that.

however, even if i had done that, that would mean i get -3.2 as a root, from factorising to x(5x + 16) = 0.

however, how would i get the root of -1.2?

thanks

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: natural log - finding both roots?

Hi,

x = -3.2  is the only solution.

---

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

mathlover002

Guest

Re: natural log - finding both roots?

hi,

ok...so how do i know when x = 0 is a solution, and when it isn't? is there a way of doing it without having to check? for example, i know ln(0) is undefined, but if i get lots of log terms in one equation then i may be able to get an equality showing that it isn't undefined, for example, combining the ln terms...

not sure. anyway, my textbook is wrong

thanks!

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: natural log - finding both roots?

Hi mathlover002,

is there a way of doing it without having to check?

I don't think so, we should always check.

---

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

Bob

Administrator

Registered: 2010-06-20

Posts: 10,164

Re: natural log - finding both roots?

hi

x = 0 ?

If you regard infinity as a number (which you shouldn't) with the property

any finite amount + infinity = infinity

then (ln 6)  - ∞ = - ∞ is 'kinda'  ok.  But you're not supposed to do that with infinity as it isn't a number.

Sometimes when an equation is manipulated 'solutions' drop out that don't fit the original problem.

I'm trying to remember / make up a good example of this.  I post again when I've got one.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

123ronnie321

Member

Registered: 2010-09-28

Posts: 128

Re: natural log - finding both roots?

Hi mathlover002,

i understand you cannot take ln of 0

Can you take ln of a negative number?

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: natural log - finding both roots?

Hi,

Can you take ln of a negative number?

Yes.

---

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

Bob

Administrator

Registered: 2010-06-20

Posts: 10,164

Re: natural log - finding both roots?

hi

As promised in post #7,  here is an equation that will seem to have two solutions:

Try to solve or look here for my solution

so it looks like x = 3 or x = -2

but only one of these values fits the original problem!

Which?

And can you see where the other one came from?

Bob

Last edited by Bob (2011-05-21 06:22:25)

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob