+33661 $$100*v_1^n=200*(5v_1)^n\\\\
100*v_1^n=200*5^n*v_1^n\\\\
1=2*5^n\\\\
$ Take logs\\
$$\ln{1}=\ln{2}+n*\ln{5}\\\\
0=\ln{2}+n*\ln{5}\\\\
n=-\frac{\ln{2}}{\ln{5}}$$
$${\mathtt{n}} = {\mathtt{\,-\,}}{\frac{{ln}{\left({\mathtt{2}}\right)}}{{ln}{\left({\mathtt{5}}\right)}}} \Rightarrow {\mathtt{n}} = -{\mathtt{0.430\: \!676\: \!558\: \!073\: \!393\: \!1}}$$
.+33661 $$100*v_1^n=200*(5v_1)^n\\\\
100*v_1^n=200*5^n*v_1^n\\\\
1=2*5^n\\\\
$ Take logs\\
$$\ln{1}=\ln{2}+n*\ln{5}\\\\
0=\ln{2}+n*\ln{5}\\\\
n=-\frac{\ln{2}}{\ln{5}}$$
$${\mathtt{n}} = {\mathtt{\,-\,}}{\frac{{ln}{\left({\mathtt{2}}\right)}}{{ln}{\left({\mathtt{5}}\right)}}} \Rightarrow {\mathtt{n}} = -{\mathtt{0.430\: \!676\: \!558\: \!073\: \!393\: \!1}}$$
