The value of x that satisfies the equation is 100.
So, none of the provided options (-83, -66, -18, -6) is the correct answer.
To find the value of x in the given equation, we need to solve for x.
The equation given is: log base 2 of the square root of x minus 2 equals 3.
Step 1: Rewrite the equation using exponential form. In exponential form, log base b of a equals c can be written as b raised to the power of c equals a.
Using this, we can rewrite the given equation as: 2 raised to the power of 3 equals the square root of x minus 2.
Step 2: Simplify the equation.
2 raised to the power of 3 equals 8. So, the equation becomes: 8 equals the square root of x minus 2.
Step 3: Isolate the square root of x by adding 2 to both sides of the equation.
8 plus 2 equals the square root of x minus 2 plus 2.
This simplifies to: 10 equals the square root of x.
Step 4: Square both sides of the equation to eliminate the square root.
(10)^2 equals (the square root of x)^2.
This simplifies to: 100 equals x.