## anonymous 4 years ago Solve 2log(x+1)-log(5x+1)+log(x-1)=log2.

1. anonymous

star with $\log(\frac{(x+1)^2(x-1)}{5x+1})=\log(2)$

2. anonymous

okay yeah i did that, i'm not sure how to move from there :S the answer is supposed to be 3.

3. anonymous

oh carp you are going to end up with a cubic polynomial. oh well...

4. anonymous

$(x+1)^2(x-1)=2(5x+1)$

5. anonymous

$x^3+x^2-11 x-3 = 0$

6. anonymous

how you are supposed to solve this is anyone's guess, but if there is a rational solution it has to be either 3 or -3 so i imagine you are supposed to try 3 and see that it works

7. anonymous

then you have to factor as $(x-3)(x^2+4x+1)$ and see that the other two zeros are negative

8. anonymous

oh so i would use quadratic formula to solve the second set?

9. anonymous

yes, but both answers are negative so you can disregard them because you would end up taking a log of a negative number, which is not defined

10. anonymous

what do you mean by "you would end up taking a log of a negative number, which is not defined", didn't we drop the logs though?