Find point of intersection for y=2(6-x) and y=2^x-2

Question

Find point of intersection. Please put answer as a coordinate point like (x,y).

Answer 1

(1) y=2(6-x)=2ˣ-2 or (2) y=2(6-x)=2ˣ⁻²?

(1) Divide through by 2: 6-x=2ˣ⁻¹-1, 7-x=2ˣ⁻¹.

We need a value of x which makes 7-x into a power of 2. So x=5 would give us 2 and the right-hand side would be 2⁴=16, so x=5 is not a solution. The next power of 2 is 4, so x=3, would make 7-x=4, and the right-hand side would be 4.  Therefore x=3 is a solution and y=2(6-3)=6. The intersection is (3,6).

(2) Divide through by 2: 6-x=2ˣ⁻³. Again, we need a value of x which makes 6-x into a power of 2. If x=2, we have 4 but -1 is the power of 2 on the right-hand side. If x=4, we have 2 on both sides, so x=4 is a solution, and y=2(6-4)=4, so the intersection is (4,4).