# Math Help - Natural Log Equation

1. ## Natural Log Equation

I have the problem

ln(c)+ln(2-c)=3
I get c=2 or c=0. Then when I plug those values in, it's wrong. Is there even a solution? Is it undefined because of the -c?
Thanks.

2. Originally Posted by dwatkins741
I have the problem

ln(c)+ln(2-c)=3
I get c=2 or c=0. Then when I plug those values in, it's wrong. Is there even a solution? Is it undefined because of the -c?
Thanks.
Since $logA+logB=log(AB)$ you can write

$log((2-c)c)=3$

$c(2-c)=e^3$

finish it..

3. Originally Posted by dwatkins741
I have the problem

ln(c)+ln(2-c)=3
I get c=2 or c=0. Then when I plug those values in, it's wrong. Is there even a solution? Is it undefined because of the -c?
Thanks.
$\log(c)+\log(2-c)=3$

$\implies \log{(c(2-c))}=3$

$\implies c(2-c)=e^3$

$\implies -c^2+ 2c- e^3 = 0$

$\frac{-2 \pm \sqrt{2^2 - 4 (-1)(- e^3)}}{2(-1)}$

You may get a complex or two.

4. Originally Posted by dwatkins741
I have the problem

ln(c)+ln(2-c)=3
I get c=2 or c=0. Then when I plug those values in, it's wrong. Is there even a solution? Is it undefined because of the -c?
Thanks.
First, there is no "-c". There is "2- c" which will be positive as long as c< 2. Second, c= 0 can't possibly be a solution specifically because ln is defined only for positive argument.

Others have shown you how to solve that. Just out of curiosity how did you "get c= 2 or c= 0"? Did you set c= 0 and 2- c= 0?