Question

Solve for x

(5√3)^x+(10√3)^(x-10)=84

Answer 1

9514 1404 393

Answer:

x = 20

Explanation:

We can define z = 3^(x/10). Then the equation is quadratic, which we can solve by completing the square. X can be found from the positive solution for z.

`z^2+(1)/(3)z=84\\\\z^2+(1)/(3)z+(1)/(36)=84(1)/(36)\\\\(z+(1)/(6))^2=(9(1)/(6))^2\\\\z=9(1)/(6)-(1)/(6)=9\\\\z=3^{(x)/(10)}=3^2\\\\x=10\cdot2\\\\\boxed{x=20}`