** Log n Grows Slowly**

The function *log(n)* grows so slowly that it can almost be
considered to be the same as 1.

A good rule: *log _{2}(1000) ≈ 10*, since

** 10 bits ≈ 3 decimal digits. **

n | log _{2}(n) | |

students in CS 314 | 240 | 8 |

students at UT | 50,000 | 16 |

people in US | 300,000,000 | 28 |

people on earth | 7,000,000,000 | 33 |

national debt | 19,500,000,000,000 | 45 |

Library of Congress, bytes | 20*10 ^{12} | 45 |

earth surface area, mm ^{2} | 5*10 ^{20} | 69 |

atoms in universe | 10 ^{80} | 266 |

Thus, we can say that *log _{2}(n) < 300* for any problem that
we are likely to see. If we simply wrote