Question

find the inverse of log5(2x+1)=g(x)

Answer 1

Is that log to base 5 or log [5(2x+1)] ?

Assuming that you mean base 5,

5^g = 2x +1
x = [5^g -1]/2

which can be written,
g^-1(x) = [5^g -1]/2
where g^-1(x) is the inverse function of g(x)