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Math

Question Find the value of xx that satisfies the equation 3=(2x+27)1/43 = (2x + 27)^{1/4}.

Studdy Solution

STEP 1

Assumptions
1. We are given the equation 3=(2x+27)143=(2x+27)^{\frac{1}{4}}.
2. We need to solve for the variable xx.

STEP 2

To solve the equation, we will first isolate the term with the variable xx by getting rid of the fourth root. We do this by raising both sides of the equation to the power of 4.
(2x+27)14=3(2x+27)^{\frac{1}{4}} = 3

STEP 3

Raise both sides of the equation to the power of 4 to eliminate the fourth root.
(2x+27)14⋅4=34(2x+27)^{\frac{1}{4} \cdot 4} = 3^4

STEP 4

Simplify both sides of the equation.
(2x+27)1=81(2x+27)^1 = 81

STEP 5

Since (2x+27)1(2x+27)^1 is simply 2x+272x+27, we can rewrite the equation as:
2x+27=812x+27 = 81

STEP 6

Now, we need to isolate xx by first subtracting 27 from both sides of the equation to move the constant term to the other side.
2x+27−27=81−272x+27-27 = 81-27

STEP 7

Simplify the equation by performing the subtraction.
2x=542x = 54

STEP 8

Finally, to solve for xx, divide both sides of the equation by 2.
2x2=542\frac{2x}{2} = \frac{54}{2}

STEP 9

Simplify the equation to find the value of xx.
x=27x = 27
The solution to the equation 3=(2x+27)143=(2x+27)^{\frac{1}{4}} is x=27x = 27.

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