# Thread: Need help solving for x

1. ## Need help solving for x

I just started a class called advanced engineering mathmatics and I guess that includes trigonometry from highschool. If anyone could help that would be great because I haven't done this stuff in years. Here are the problems:
Solve for x:

18cos^2x + 3cosx - 1 = 0

cosx + 3sinx = 1

13^(3x) * 4^(2x) = 5

Thanks for any help in advance, this wouldn't be a problem if the book wasn't sold out at the bookstore.

2. Originally Posted by nafix
I just started a class called advanced engineering mathmatics and I guess that includes trigonometry from highschool. If anyone could help that would be great because I haven't done this stuff in years. Here are the problems:
Solve for x:

18cos^2x + 3cosx - 1 = 0

cosx + 3sinx = 1

13^(3x) * 4^(2x) = 5

Thanks for any help in advance, this wouldn't be a problem if the book wasn't sold out at the bookstore.
1) Let $\displaystyle y=cos(x)$; use the quadratic equation to solve for y, and then solve for x

2) x = 0

3)
$\displaystyle 13^{3x} * 4^{2x} = 5$

$\displaystyle 2197^x 16^x = 5$

$\displaystyle (2197*16)^x = 5$

$\displaystyle ln(2197*16)x = ln(5)$

$\displaystyle 10.47x = 1.61$

$\displaystyle x = .154$

3. Much appreciated Colby.