Question

Solve for x (5√3)^x+(10√3)^(x-10)=84

Answer 1

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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.

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