Solve 2log(x+1)-log(5x+1)+log(x-1)=log2.

Question

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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?