I read this as y=6x+2.
ln(y)=(x+2)ln(6) or log6(y)=x+2.
x+2=ln(y)/ln(6), x=ln(y)/ln(6)-2; or x=log6(y)-2⇒ln(y)/ln(6)=log6(y).
We can write x=g(y) and y=f(x).
g(y)=ln(y)/ln(6)-2, therefore g(x)=ln(x)/ln(6)-2 (or g(x)=log6(x)-2).
f(x)=6x+2, g(x)=ln(x)/ln(6)-2; but g(x)=f-1(x)=ln(x)/ln(6)-2 or log6(x)-2.
f-1(x) is the inverse function: f(f-1(x))=6(log₆(x)-2)+2=6log₆(x)=x;
also f-1(f(x))=log6(f(x))-2=log6(6x+2)-2=x+2-2=x.