## Problem of the Day #375: Log Entry 00March 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.