It is known that the range of function y = Log1 (2 ^ x-a + 2) is r, a

It is known that the range of function y = Log1 (2 ^ x-a + 2) is r, a

The necessary and sufficient condition for log logarithm function to be r is that the function in brackets can get all positive numbers (refer to function image)
2 ^ x-a + 2 can be seen as an increasing function (refer to the image), so as long as its minimum value is less than or equal to 0, it can get all positive numbers
And because the minimum value of 2 ^ x is infinitely close to 0 (reference image), the minimum value of the whole formula is infinitely close to - A + 2
So as long as - A + 2 is less than or equal to 0, that is, a is greater than or equal to 2