To find the values of x for which the given inequality holds true, we can first determine when the expression (x-2)^(x^2-6x+8) equals 1.
When (x-2)^(x^2-6x+8) equals 1, this means that the base (x-2) must be equal to 1, and the exponent (x^2-6x+8) can be any integer value.
Therefore, we have:
x - 2 = 1 x = 3
Now, we need to consider when the expression is greater than 1. Since the base (x-2) is greater than 1 for x > 3, the expression will always be greater than 1 for x > 3.
Therefore, the solutions to the inequality (x-2)^(x^2-6x+8) > 1 are all real numbers greater than 3, or simply x > 3.
To find the values of x for which the given inequality holds true, we can first determine when the expression (x-2)^(x^2-6x+8) equals 1.
When (x-2)^(x^2-6x+8) equals 1, this means that the base (x-2) must be equal to 1, and the exponent (x^2-6x+8) can be any integer value.
Therefore, we have:
x - 2 = 1
x = 3
Now, we need to consider when the expression is greater than 1. Since the base (x-2) is greater than 1 for x > 3, the expression will always be greater than 1 for x > 3.
Therefore, the solutions to the inequality (x-2)^(x^2-6x+8) > 1 are all real numbers greater than 3, or simply x > 3.