# simplifying logs

• Nov 25th 2012, 11:21 AM
kingsolomonsgrave
simplifying logs
 Solve the equation: https://mapleta.wlu.ca/mapleta/tmp/d...hbdeachppg.gif https://mapleta.wlu.ca/mapleta/tmp/m...ifmbnbkchn.gif

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)
• Nov 25th 2012, 11:32 AM
grillage
Re: simplifying logs
Start by simplifying the left hand side using the law of logarithms: log(x) + log(y) = log(xy)
• Nov 25th 2012, 11:34 AM
kingsolomonsgrave
Re: simplifying logs
I get x^2+12x+29=0 but how to factor that since 29 is prime?
• Nov 25th 2012, 11:34 AM
grillage
Re: simplifying logs
• Nov 25th 2012, 11:37 AM
grillage
Re: simplifying logs
Just as a reminder:

$\displaystyle x=\frac{-b\pm \sqrt{b^{2}-4ac}}{2a}$
• Nov 25th 2012, 12:26 PM
skeeter
Re: simplifying logs
Quote:

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

complete the square ...

$\displaystyle x^2+12x = -29$

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

$\displaystyle (x + 6)^2 = 7$

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

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

since $\displaystyle x > -4$ ...

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