one week before an examination day a librarian monitored the number of students who visited the library then they compared it with the number of visits made in an average week approximately 2×10 to the power of three visits were reflected in their logbook during this one week. While only about 5×10 to the power of two were reflected on an average week, how many times higher is the number of library visits before the examination day compared to the library visits in an average week your answer should be a whole number.

To find how many times higher the number of library visits before the examination day is compared to the average week, we can divide the two values:

1. The number of visits one week before the examination: \( 2 \times 10^3 \)
2. The average number of visits in a week: \( 5 \times 10^2 \)

Now, we divide the number of visits before the examination day by the average number of visits:

\[ \text{Ratio} = \frac{2 \times 10^3}{5 \times 10^2} \]

First, simplify the expression:

\[ \text{Ratio} = \frac{2}{5} \times \frac{10^3}{10^2} \]

Now calculate \( \frac{10^3}{10^2} = 10^{3-2} = 10^1 = 10 \).

So the ratio becomes:

\[ \text{Ratio} = \frac{2}{5} \times 10 \]

Now, calculate:

\[ \frac{2 \times 10}{5} = \frac{20}{5} = 4 \]

Therefore, the number of library visits one week before the examination day is 4 times higher than the average number of visits in a week. Thus, the final answer is:

\[ \boxed{4} \]