Compare $2^{2016}$ and $10^{605}$ without a calculator So, I am supposed to compare $2^{2016}$ and $10^{605}$ without using a calculator, I have tried  division by $2$ on both sides  and then comparing $2^{1411}$ and $5^{605}$, and then substituting with $8,16,10$ and then raising to powers and trying to prove that but that did not go anywhere, I have also tried taking $\log$ of both sides, but did not help either. Also is there a more general approach to these kind of problems?

\begin{aligned}
2 ^ {2016} > 10 ^ {605} & \iff \\
e ^ {\ln (2 ^ {2016}) } > e ^ {\ln (10 ^ {605}) } & \iff \\
\ln (2 ^ {2016}) > \ln (10 ^ {605}) & \iff \\
2016 \cdot \ln (2) > 605 \cdot \ln (10) & \iff \\
\frac{2016}{605} > \frac{\ln 10}{\ln 2} & \iff \\
\frac{2016}{605} > \frac{\log 10}{\log 2} & \iff \\
\frac{2016}{605} > \frac{1}{\log 2} & \iff \\
3.33 \ldots > \frac{1}{0.301 \ldots} & \iff \\
3.33 \ldots > 3.32 \ldots
\end{aligned}
PS: the two boxed expressions (i.e $\boxed{ \frac{2016}{605} }$ and $\boxed{ \log 2}$ ) can be derived by hand: one can divide on paper and (as far as I can remember) during tests you can bring logarithmic tables
