How large is $2^{100}$, and what is its starting digit?

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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

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

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

3. \(2^{100}\) begins in a \(1\) and is \(31\) digits long;

4. \(2^{100}\) begins in a \(2\) and is \(31\) digits long.