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Authors:
Walter Savitch ,julia Lobur
Chapter:
Standard Template Library
Exercise:
Self-test Exercises
Question:18 | ISBN:9780321531346 | Edition: 7

Question

Show that for any two bases a and b for logarithms, if a and b are both

greater than 1, then there is a constant c such that loga N ≤ c(logb N).

Thus, there is no need to specify a base in O(log N). That is, O(loga N)

and O(logb N) mean the same thing.

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Answer

This is mathematics, not C++. So, = will mean equals not assignment.

First note that loga N = (loga b)(logb N).


To see this first identity just note that if you raise a to the power loga N

you get N and if you raise a to the power (loga b)(logb N) you also get N.

If you set c = (log a b) you get log a N = c(log b N).

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