Integration with logs

[Skelly4444]

Having trouble getting the same answer as the book on this one when I integrate it?

-1/3ln|3x-2| = t/100 -1/3ln|-2|

The answer in the book is x=1/3(2-2e to the power-3t/100)

I agree with this answer except I have a positive sign between the 2 and 2e instead of their negative.

 

[BigBeachBanana]

Could you share your work? We can help you find why that is.

 

[pka]

Having trouble getting the same answer as the book on this one when I integrate it?
-1/3ln|3x-2| = t/100 -1/3ln|-2|
The answer in the book is x=1/3(2-2e to the power-3t/100)
I agree with this answer except I have a positive sign between the 2 and 2e instead of their negative.

To Skelly, please post the entire original question as given to you.

 

[topsquark]

Having trouble getting the same answer as the book on this one when I integrate it?

-1/3ln|3x-2| = t/100 -1/3ln|-2|

The answer in the book is x=1/3(2-2e to the power-3t/100)

I agree with this answer except I have a positive sign between the 2 and 2e instead of their negative.

To make it easier to read and write: [imath]x^3[/imath] is x^3.

-Dan

 

[Dr.Peterson]

Having trouble getting the same answer as the book on this one when I integrate it?

-1/3ln|3x-2| = t/100 -1/3ln|-2|

The answer in the book is x=1/3(2-2e to the power-3t/100)

I agree with this answer except I have a positive sign between the 2 and 2e instead of their negative.

It appears that the problem has nothing to do with integration! What you are doing is solving for x.

According to Wolfram Alpha, there are two solutions, yours and theirs! (I checked that first, to see if I was interpreting the problem correctly.) I, too, get [imath]x=\frac{1}{3}\left(2\pm2e^{-3t/100}\right)[/imath].

So, we really need to see the entire problem to see if you have omitted something. (I'm also very curious why they say [imath]\ln|-2|[/imath] rather than [imath]\ln(2)[/imath].) My guess is that this is a final step in solving a differential equation, and there are some conditions that will determine the choice of solution.

There are reasons we ask you to show us the original problem, not just the part you're working on!