Question 13943 – Algorithms

A microsecond is 10⁻⁶ seconds. Hence, one second = 10⁶ microseconds, one hour = 3600000000 = 3.6 · 10⁹ microseconds, one month (assume a month has 30 days) = 2592000000000 = 2.592 · 10¹² microseconds, and one century = 3110400000000000 = 3.1104 · 10¹⁵ microseconds.
f(n) = log n In this case, we need to determine the largest n such that log n ≤ 1000000. To solve this inequality, we need to rewrite the inequality as 2^logn ≤ 2 ^1000000 or n ≤ 2 ^1000000.
2¹⁰ ≈ 10³ , thus we have that 2^1000000 = 2^10·100000 = (2¹⁰) ¹⁰⁰⁰⁰⁰ ≈ (10³ ) ¹⁰⁰⁰⁰⁰ = 10³⁰⁰⁰⁰⁰