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Problem of the Day #375: Log Entry 00 March 28, 2012

Posted by Albert in : potd , trackback

Alex has decided to provide you with the following data:

$$
\begin{eqnarray}
\ln(2) & \approx & 0.693147181 \\
\ln(3) & \approx & 1.09861229 \\
\ln(5) & \approx & 1.60943791 \\
\ln(7) & \approx & 1.94591015
\end{eqnarray}
$$

Your mission, should you choose to accept it, is to find the smallest positive integer $x$ such that $2^{10 x}$ has more than $3x+1$ digits.

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