Answer:
x = 19683 or x = 0
Step-by-step explanation:
Solve for x:
2 x = 54 x^(2/3)
Hint: | Isolate the radical to the left hand side by reversing the equality.
2 x = 54 x^(2/3) is equivalent to 54 x^(2/3) = 2 x:
54 x^(2/3) = 2 x
Hint: | Eliminate the power on the left hand side.
Raise both sides to the power of three:
157464 x^2 = 8 x^3
Hint: | Move everything to the left hand side.
Subtract 8 x^3 from both sides:
157464 x^2 - 8 x^3 = 0
Hint: | Factor the left hand side.
Factor x^2 and constant terms from the left hand side:
-8 x^2 (x - 19683) = 0
Hint: | Divide both sides by a constant to simplify the equation.
Divide both sides by -8:
x^2 (x - 19683) = 0
Hint: | Find the roots of each term in the product separately.
Split into two equations:
x - 19683 = 0 or x^2 = 0
Hint: | Look at the first equation: Solve for x.
Add 19683 to both sides:
x = 19683 or x^2 = 0
Hint: | Look at the second equation: Eliminate the exponent.
Take the square root of both sides:
Answer: x = 19683 or x = 0
