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What is the value of x if log in base 2 of the quantity square root of x minus 2 end quantity equals 3 question mark

-83
-66
-18
-6

User Kioli
by
8.7k points

1 Answer

4 votes

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.

User Nerea
by
8.3k points

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