Question

Solve the logarithmic equation:

log_2(x^2 - x - 2) = 2

A) x = -1
B) x = 2
C) x = -2
D) x = 3

Answer 1

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.