1. ## simplifying logs

 Solve the equation:

can someone explain how I would obtain the answer above? I know how to actually solve for x numerically, but I don't know how to get -6+7^(1/2)

2. ## Re: simplifying logs

Start by simplifying the left hand side using the law of logarithms: log(x) + log(y) = log(xy)

3. ## Re: simplifying logs

I get x^2+12x+29=0 but how to factor that since 29 is prime?

5. ## Re: simplifying logs

Just as a reminder:

$x=\frac{-b\pm \sqrt{b^{2}-4ac}}{2a}$

6. ## Re: simplifying logs

Originally Posted by kingsolomonsgrave
I get x^2+12x+29=0 but how to factor that since 29 is prime?
complete the square ...

$x^2+12x = -29$

$x^2 + 12x + 36 = 36-29$

$(x + 6)^2 = 7$

$x+6 = \pm \sqrt{7}$

$x = -6 \pm \sqrt{7}$

since $x > -4$ ...

$x = -6 + \sqrt{7}$