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The problem is:

Given a number, find out if this number could be the beginning digits of a 2 exponent & if it can output which power it can be.

As an example given 2 there is answer $8$ which $2 ^ 8 = 256$ which begins with $2$ -> the number given.

Thanks.

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    what? ${}{}{}{}{}$ – 2017-01-25
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    Do you mean the following: Given a number $n$ find if there is a value $k$ such that the last digits of $2^k$ form the number $n$? – 2017-01-25
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    no, I meant the first digits. sorry for ambiguity :) – 2017-01-25

1 Answers 1

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Such a number always exists,suppose $n$ is the given number, you just need to find an integer $a$ such that the fractional part of $a\log_{10}2$ approximates the fractional part of $\log_{10}(n)$ from above sufficiently well.

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    could you please explain this in an example? – 2017-01-25