Question
Which of the following should be done to both sides of the equation x12=6 to solve the value of x ?(1 point)
Responses
multiply by 6
multiply by 6
multiply by −12
multiply by negative 12
multiply by 12
multiply by 12
divide by 12
To solve for the value of x in the equation x^12 = 6, you should take the 12th root of both sides of the equation.
To solve for the value of x in the equation x^12 = 6, you should divide both sides of the equation by 12. Therefore, the correct response is "divide by 12."
To solve for the value of x in the equation x^12 = 6, you need to perform the same operation on both sides of the equation. In this case, you should take the 12th root of both sides, since the exponent on x is 12.
Here's how you do it:
1. Take the 12th root of both sides of the equation. This can be expressed as (x^12)^(1/12) = 6^(1/12).
2. Simplify the left side of the equation by applying the power of a power rule. (x^12)^(1/12) can be rewritten as x^(12 * 1/12).
3. Simplify further by cancelling out the exponent of 12 and 1/12. This leaves you with x^1, which is simply x.
4. Simplify the right side of the equation by evaluating 6^(1/12) on a calculator. The approximate value is 1.4678.
5. The equation x = 1.4678 is the solution to the original equation x^12 = 6.
Therefore, the correct operation to perform on both sides of the equation is to take the 12th root (or raise to the power of 1/12). None of the other operations listed (multiplying by 6, multiplying by -12, multiplying by 12, or dividing by 12) will give you the correct solution.