Question

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 :(

Answer 1

I am also stuck just as you are.

Answer 2

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,, =)