Final answer:
To solve the logarithmic equation log_2(x^2 - x - 2) = 2, we rearrange it into a quadratic equation and solve for x using the quadratic formula. The solutions are x = 3 and x = -2. The correct answer is option D.
Step-by-step explanation:
The given equation is:
log2(x2 - x - 2) = 2
To solve this equation, we need to use the property that states:
The logarithm of the number resulting from the division of two numbers is the difference between the logarithms of the two numbers.
So, we rewrite the equation as:
x2 - x - 2 = 22
2 - x - 2 = 4
Now we can rearrange this into a quadratic equation:
x2 - x - 6 = 0
Using the quadratic formula, we can solve for the two possible values of x:
x = 3 or x = -2
Therefore, the solutions to the logarithmic equation are x = 3 and x = -2.