Logarithmic and Quadratic Functions (Parabola)

First, consider that the parabolic opening is upward (the x 2 coefficient is positive).

Secondly, the composite result is the increasing function in the interval (2, positive infinity).

So the logarithm must also increase, that is, a >；; 1

The range of parabolic symmetry axis is X≤2.

x≤-B/2A a≤2

Missing a condition, x2-2ax+3 >; So the parabola can only be above the x axis.

Discriminant is less than 0 a

therefore

1< a< root number 3

7/4 is the value of a when the parabola intersects the X axis at point (2,0), but X 2-2ax+3 can only be greater than 0, but not equal to 0.