4\^x - 4\^(x-1) = 4\^x - (1/4)\*4\^x = (3/4)\*4\^x

3\^(x+1) - 3\^x = 3\*3\^x - 3\^x = 2\*3\^x

So, now you have:

(3/4)\*4\^x = 2\*3\^x

Now solve with logs. Note that log(8/3)=-log(3/8) and log(3/4)=-log(4/3), which migh come in handy depending on you proceed.