Posted by **Neee** on Thursday, August 12, 2010 at 6:37pm.

Solve the given equation:

ln(x + 4) + ln(x + 2) = 2

ps - we aren't allowed calculators

My ans:

I got as far as

ln [(x+4)(x+2)] = 2

ln (x^2+6x+8) = 2

And then I am lost, whatever I do ends up with no answer.

I also rewrote the above so that it is

e^2 = x^2+6x+8

But of course that made it worse :(

- Maths -
**Damon**, Thursday, August 12, 2010 at 8:19pm
I am also stuck just as you are.

- Maths -
**jai**, Friday, August 13, 2010 at 5:04am
i also got the same equation:

ln [(x+4)(x+2)] = 2

ln (x^2+6x+8) = 2

x^2+6x+8 = e^2

x^2+6x+(8-e^2)=0

thus, you have no choice but to use quadratic formula: (where a=1, b=6, c=8-e^2)

[-6+-sqrt(6^2-4(1)(8-e^2))]/2(1)

[-6+-sqrt(36-32+4e^2)]/2

[-6+-sqrt(4+4e^2)]/2 *factor out 4

[-6+-2(sqrt{1+e^2})]/2

therefore, x is equal to:

-3+sqrt(1+e^2) and -3-sqrt(1+e^2)

so there,, =)

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