Question

log2(7x+1)=log2(2-x)

Answer 1

Since you have the same log operation on both sides, you simply have
7x+1=2-x

Answer 2

(Just think of why: when you solve some equations, you log both sides of the equation right? (with the same base for the log) And the equation still holds true. So, here your equation is already "logged" on both sides, so un-logging both sides would still be equal :) )