Solve 2x=54xˆ(2/3)

Please, I need the step by step working to find the value of x

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:

x = 19683 or x = 0

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