Is $\frac{\ln2^{n+1}}{1}$ equal to $\frac{\ln2^{n}*\ln2^{1}}{1}$ or $\frac{\ln2^{n}2^{1}}{1}$

Question

Well i am not sure about this. I have something like this $$\frac{\ln2^{n+1}}{1}$$ And i dont know what is corret can i extend it like this? $$\frac{\ln2^{n}*\ln2^{1}}{1}$$ Or this one is correct? $$\frac{\ln2^{n}2^{1}}{1}$$

Answer 1

Note that for $a,b>0$, we have that $$ \ln(ab)=\ln(a)+\ln(b). $$ In particular $$ \ln(2^{n+1})=\ln(2^n\times 2)=\ln(2^n)+\ln 2 $$