9514 1404 393
Answer:
x = 20
Step-by-step 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.
[tex]z^2+\dfrac{1}{3}z=84\\\\z^2+\dfrac{1}{3}z+\dfrac{1}{36}=84\dfrac{1}{36}\\\\(z+\dfrac{1}{6})^2=(9\dfrac{1}{6})^2\\\\z=9\dfrac{1}{6}-\dfrac{1}{6}=9\\\\z=3^{\frac{x}{10}}=3^2\\\\x=10\cdot2\\\\\boxed{x=20}[/tex]
