PA of Algorithms Q62

0. Two alternative packages A and B are available for processing a database having 10^k records. Package A requires 0.0001 n² time units and package B requires 10nlog₁₀n time units to process n records. What is the smallest value of k for which package B will be preferred over A?

Answer
Comment
Array

Option : C
Explanation :
B must be preferred on A as
0.0001 n² < 10 n log₁₀ n
⇒ 10^-5 n < log₁₀n
⇒ 10^-5 < log₁₀n^1/n
⇒ n 10^-5 < log₁₀n
We know log₁₀n = k
⇒ 10^k = t
⇒ k > 10^-5 10^k
⇒ k > 10^k-5
⇒ k – 5 > 0
⇒ k > 5
Then min k = 6

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