Let p denotes the prefix, T Denotes the # of lost digits. We are searching for N, that the prefix of 2 ^ N is P.
We have an inequlity
P * 10 ^ t Thus
Log2 (p * 10 ^ t) Which is
Log2 (p) + T * log2 (10) Also, we know that
P That is
T> log10 (p) +
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