I need some math help

[Dustin_m]

I'm stuck on a problem here. It's not complicated, but i cant figure it out

I need to solve this:

e^(2x)+24=11e^x

The thing that screws me up is the 24 in there. if i move that to the right side and the 11e^x to the left, is that correct? I would have e^(2x)-11e^x=-24 . Can i LN both sides of that?

 

[Citizen_Insane]

Ok, so first look at it like a regular trinomial. Remember that e^(2x) = (e^x)^2. Therefore:

(e^x)^2-11e^x+24=0. Subsitute y = e^x:

y^2-11y+24=0
(y-8)(y-3)=0

Your roots are 8 and 3. So, replacing y with e^x:

e^x=8, and e^x=3
x = ln(8) and x=ln(3)

 

[Dustin_m]

Ahh, ok. I got it now.

Thanks

 

[Citizen_Insane]

Np man.