Answer:
the log of the first equation gives the second
Explanation:
You want to know why ...

means ...

Logarithms
Taking logs to the base 2 of the original equation, we get ...

__
Additional comment
This is the relation you asked about. It can be solved by taking logs one more time (base 2).
4x = 2 +x
3x = 2 . . . . . . . subtract x
x = 2/3 . . . . . . . divide by 3
This is the only value of x for which all of these exponential expressions have the relations given.
The relevant log relation is ...
log(a^b) = b·log(a)