The property states that log[a]b+log[a]c=log[a](b*c)
Therefore:

log[5](2x+1)+log[5](3)
=log[5]((2x+1)(3))
=log[5](6x+3)

step 2:

Just put both sides of the equation in the exponent part of a base that matches the base in the logarithim…in this case it’s 5.

log[5]6=log[5](6x+3)
5^(log[5]6)=5^(log[5](6x+3))

the 5^ and the log[5] cancel each other out now

step 3:

6=6x+3
6x+3=6
6x=3
x=1/2