I need help on question no. 2 Oct/Nov 2009 pure math 3

[osmosis]

can anyone help me how to find the two consecutive integers for question no.2 OCT/NOV 2009 pure math 3 paper???

[osmosis]

do we need to just substitute any integer??? or is there any other way to get x=3 and x=4???

[astarmathsandphysics]

Will answer when I get up

[astarmathsandphysics]

3^(x+2)=3^x+3^2
3^(x+2)-3^x=3^2
3^x(3^2-1)=3^2
3^x=3^2/(3^2-1)
xln3=ln(3^2/(3^2-1))
x=ln(3^2/(3^2-1)))/ln3

[osmosis]

owh...that is for paper 31.... mine is paper 32....about finding the two consecutive integers on numerical solution topic.....that's where I got problem in finding the integer...can you help me with that one?

[astarmathsandphysics]

How did I miss that? When I get home.

[astarmathsandphysics]

Trial and error. The root is between 3 an 4
f(3)<0 f(4)>0
so between 3 and 4 there is a sign change and a root.

[osmosis]

ok....thank you so much!