Hi Gyrst, it is nice to meet you :)
G = y 1-(1+r)^-n/r
\(G = y_1-\frac{(1+r)^{-n}}{r}\\ G - y_1=-\frac{(1+r)^{-n}}{r}\\ -r(G - y_1)=(1+r)^{-n}\\ (ry_1-Gr)=(1+r)^{-n}\\ ln(ry_1-Gr)=ln(1+r)^{-n}\\ log(ry_1-Gr)=log(1+r)^{-n}\\ log(ry_1-Gr)=-nlog(1+r)\\ \frac{log(ry_1-Gr)}{log(1+r)}=-n\\ -n=\frac{log(ry_1-Gr)}{log(1+r)}\\ \)