simplifying logs

**kingsolomonsgrave** · November 25th 2012, 11:21 AM

Solve the equation:

Correct Answer:	-6+7^(1/2)

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)

**grillage** · November 25th 2012, 11:32 AM

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

**kingsolomonsgrave** · November 25th 2012, 11:34 AM

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

**grillage** · November 25th 2012, 11:34 AM

Use the quadratic formula

**grillage** · November 25th 2012, 11:37 AM

Just as a reminder:

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

**skeeter** · November 25th 2012, 12:26 PM

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 $x > -4$ ...

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

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