To solve this equation, we need to first rewrite the equation using the properties of logarithms.
Using the property log_a(b) = log_a(c) if and only if b=c, we can rewrite the equation as:
x^2 - x - 2 = 3 - x^2 + 2x
Now, we simplify the equation by combining like terms and rearranging:
x^2 - x - 2 = 3 - x^2 + 2 2x^2 - 3x - 5 = 0
Now, we have a quadratic equation in the form of ax^2 + bx + c = 0. We can solve this equation by factoring, completing the square, or using the quadratic formula. Let's use the quadratic formula:
x = (-(-3) ± √((-3)^2 - 4(2)(-5))) / (2(2) x = (3 ± √(9 + 40)) / x = (3 ± √49) / x = (3 ± 7) / 4
Therefore, the solutions to the equation are x = 5/2 or x = -1.
To solve this equation, we need to first rewrite the equation using the properties of logarithms.
Using the property log_a(b) = log_a(c) if and only if b=c, we can rewrite the equation as:
x^2 - x - 2 = 3 - x^2 + 2x
Now, we simplify the equation by combining like terms and rearranging:
x^2 - x - 2 = 3 - x^2 + 2
2x^2 - 3x - 5 = 0
Now, we have a quadratic equation in the form of ax^2 + bx + c = 0. We can solve this equation by factoring, completing the square, or using the quadratic formula. Let's use the quadratic formula:
x = (-(-3) ± √((-3)^2 - 4(2)(-5))) / (2(2)
x = (3 ± √(9 + 40)) /
x = (3 ± √49) /
x = (3 ± 7) / 4
Therefore, the solutions to the equation are x = 5/2 or x = -1.