2^y = 2 - 2^x
taking log:
ylog2 = log (2-2^x)

y = log (2-2^x)  with base 2.

Now, properties for log t  are:

1)t>0

2) base should be positive and not equal to 1. (which is 2 in our case)

So, 2-2^x >0

=> 2 > 2^x

=> x<1. (domain)