1 = log4(4)
Thus, we have
log4(2x+1) + log4(4) = log4(x+5)
The sum of logs equals the log of their product.
log4[(2x+1) (4)] = log4(x+5)
Thus, we set the two terms, which are both to the log4, equal.
(If you prefer, calculate 4 to the power of both sides to remove the log)
Then, (2x+1)(4) = x+5
8x+4 = x + 5
7x = 1
x = 1/7
Note that x+5 and 2x+1 are positive. Thus, there are no issues with taking the log.