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Alevel maths c3 help

How do you solve:
ln(x2+5x+6) - ln(x2+3x)=3
Use the rule:
ln(a) - ln(b) ≡ ln(a/b)
Thanks, however the answer states that the answer is x=2/e3 - 1??
Original post by computerwizz
How do you solve:
ln(x2+5x+6) - ln(x2+3x)=3


Applying log rules, you get ln[(x2+5x+6)/(x2+3x)]=3
Factorise (x2+5x+6) and you get (x+2)(x+3).
Factorise (x2+3x) and you get x(x+3)
Therefore x2+5x+6)/(x2+3x)=(x+2)/x as common factors eliminate.

ln[(x+2)/x]=3

3=ln(e^3)

This gives (x+2)/x = e^3.
EDIT: I accidentally multiplied this out. It should be 1+(2/x)=e^3. You can then rearrange.
(edited 6 years ago)
Original post by JemmaSimmons
Applying log rules, you get ln[(x2+5x+6)/(x2+3x)]=3
Factorise (x2+5x+6) and you get (x+2)(x+3).
Factorise (x2+3x) and you get x(x+3)
Therefore x2+5x+6)/(x2+3x)=(x+2)/x as common factors eliminate.

ln[(x+2)/x]=3

3=ln(e^3)

This gives (x+2)/x = e^3.
x^2+2x=e^

x^2+2x-e^3 =0.

Use quadratic formula to solve. :smile:


Thanks, however the answer states that it
is x=2/e3 - 1??
Original post by jbiard
ln(x^2+5x+6) - ln(x^2+3x)=3
ln( (x^2+5x+6)/(x^2+3x) ) =3
(x^2+5x+6)/(x^2+3x)=e^3

(x^2+5x+6)= e^3(x^2+3x)

(1-e^3)x^2 + (5-3e^3)x +6 = 0

X= 0.104791393 ,


Don't do this ever again. Never post full answers on TSR. Delete it before you receive a notice.
Original post by JemmaSimmons
Is that 2 over (e^3-1)?


Yes!
Reply 7
Avatar for TasnimCh
TasnimCh
1
ln(x^2+5x+6) - ln(x^2+3x)=3
ln(X+3)(x+2)/x(X+3)=3
(X+2)/x=e^3
x+2=xe^3
2=xe^3-x
factorise and rearrange
(edited 6 years ago)
Reply 8
Avatar for jbiard
jbiard
3
Original post by Rohit_Rocks10
Don't do this ever again. Never post full answers on TSR. Delete it before you receive a notice.


woah why??
Original post by jbiard
woah why??


Much better to hint the person to the right answer rather than give them the full solution.
Original post by TasnimCh
ln(x^2+5x+6) - ln(x^2+3x)=3
ln(X+3)(x+2)/x(X+3)=3
(X+2)/x=e^3
x+2=xe^3
2=xe^3-x
factorise and rearrange



Thanks! :smile:
Reply 11
Avatar for jbiard
jbiard
3
Original post by RDKGames
Much better to hint the person to the right answer rather than give them the full solution.


cool, but why would i get a notice?!
Original post by jbiard
cool, but why would i get a notice?!


Because it's part of the maths forum's rules not to give out a full solution unless OP doesn't understand after a suitable number of hints.
Original post by computerwizz
Thanks! :smile:


No worries dude :smile:
Reply 14
Avatar for jbiard
jbiard
3
Original post by RDKGames
Because it's part of the maths forum's rules not to give out a full solution unless OP doesn't understand after a suitable number of hints.


yeah i just read the maths forum rules, didnt realise you werent aloud to give full worked solutions before, sorry!

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