Hey!
It's been years since I've done calculus and can't believe I can't remember how to do something like this.
Can anyone help?

I assume the directions would be to solve for "x".

ln(x+4) - ln(x+2) = ln(x)

Using some of the properties, couldn't you rewrite that like this:
ln [ (x+4) / (x+2) ] = ln(x)

Here's the point where I get stuck. What I'm pretty sure you can't do is break up the pieces (ie: you can't say ln(x)*ln(4) for ln(x+4) )

Ideas?
Thanks!

~Kim~
PS...in case anyone's wondering, this isn't my homework. I'm out of college & just am doing this to see if I remember - which apparently, I don't!

 

use e^x...

Meaning, you take both sides and raise them to e^x

x = ln[(x+4)/x+2)] for the left
x = ln(x) for the right

You should be able to figure out the rest

 

eridia78, I'm in Hollywood (FL) too.

Ok - anyway....using that, I have this:

(x+4)/(x+2) = x

Multiplying both sides by (x+2), I have this now:
(x+4) = (x)*(x+2)
x + 4 = x^2 + 2x

0 = x^2 + 1x - 4

Can't be factored, so use the quad. equation to solve for x.

Am I on the right track?

~Kim~

 

Quadratic formula. (The thing you're solving is a quadratic equation.)

Yes, you're on the right track.

By the way, you'll get two solutions to the quadratic equation, only one of which is valid in the original equation. Any idea why?

 

Because the negative answer will make the original equation undefined?

 

Bingo! Nonpositive numbers do not have (real) logarithms.

By the way, this is algebra, not calculus.

 

actually, it's pre -calculus

Quick2K

 

But it belongs to the algebraic classification, not Calculus. I suppose that when you take single-variable Calculus, they'll make you review logs and natural logs. So that's where the confusion takes place.

 

Hey everyone!
Thanks for the assistance! It's been years since I did this stuff. I have some random girl from FAU who IMs me every now & then w/ a problem she picked up in class (Calculus I) and I like to see if I remember how to do it.

Magician, I did mean to write "quadratic formula" (not equation) - thanks for bringing that up. Hopefully now I won't forget!

God - I've got to start teaching this stuff so it sticks!
We've got some smart people on here!


~Kim~

 

[QUOTE]Originally posted by CutieBonny
But it belongs to the algebraic classification, not Calculus.