Solution
For this case we have the following equation:
[tex]2^{n+1}=\frac{1}{8}[/tex]And we can do the following:
[tex]\frac{2^n}{2}=\frac{1}{8}[/tex]Solving for n we have:
[tex]2^n=\frac{1}{4}[/tex]Then we can apply natural log on both sides and we got:
[tex]n\ln (2)=\ln (\frac{1}{4})[/tex][tex]n=\frac{\ln (0.25)}{\ln (2)}=-4[/tex]