Given that \[\log_{10} 2 = 0.3010 \; \text{ (to }4\text{ d.p.)}\] and that \[10^{0.2} < 2\] it is possible to deduce that

\(2^{100}\) begins in a \(1\) and is \(30\) digits long;

\(2^{100}\) begins in a \(2\) and is \(30\) digits long;

\(2^{100}\) begins in a \(1\) and is \(31\) digits long;

\(2^{100}\) begins in a \(2\) and is \(31\) digits long.