simplifying logs

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November 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

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)
November 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)
November 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?
November 25th 2012, 11:34 AM
grillage

Re: simplifying logs

Use the quadratic formula
November 25th 2012, 11:37 AM
grillage

Re: simplifying logs

Just as a reminder:

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

$x^2+12x = -29$

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

$(x + 6)^2 = 7$

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

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

since $x > -4$ ...

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

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