Question

Solve 4x² = 12 for x using the change of base formula

a) x=√3
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b) x=−√3
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c) x=2
d) x=−2

Answer 1

To solve 4x² = 12, divide by 4 to get x² = 3, then take the square root of both sides to obtain x = √3 or x = -√3. The correct options are both A&B .

Step-by-step explanation:

To solve the equation 4x² = 12 for x, we need to isolate x. First, we can divide both sides of the equation by 4 to simplify the equation to x² = 3. Taking the square root of both sides of the equation gives us two possible solutions, since a square root can be both positive and negative. Hence, x can be √3 or -√3.

1. Divide both sides by 4: x² = 3.
2. Take the square root of both sides: x = ±√3.
3. We have two solutions: x = √3 and x = -√3.

This follows from the basic algebraic principles of solving quadratic equations, as seen in various examples like x² + 1.2 x 10-2x -6.0 × 10-3 = 0 or (2x)² = 4.0 (1 - x)², which can be solved using similar algebraic manipulations or using the quadratic formula for more complex cases.

Given the equation 4x² = 12, we can solve for x using the change of base formula.

First, we divide both sides of the equation by 4 to isolate x²: x² = 12/4 = 3.

Next, we take the square root of both sides to solve for x: x = ±√3.

Therefore, the solutions to the equation are x = √3 and x = -√3.