domain is x<1.

the domain should be x<1

yup domain is x <1 check here

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)

@ Himanshu...

Dear U took log in the question and defined its Domain....

In this manner every Domain will be restricted as Log has its own Domain....

This is not the right method..

the domain can be logically caluted saying that both 2^x and 2^y are +ve no. thrfr none can exceed 2..

thrfr each one can extent upto 1 only infact it cant take the value 1 as the other cant be nil......

and they have no lower limit................ thrfr its <1...!!!

ans!!!