Running Time of a d-ary heap?

Question

How is the running time of a d-Ary heap simplified from O(log_d n) to O( (log n) / (log d))?

A correct simplification would be: log_dn = log d * log n

How is the division simplification derived?

Answer 1

This uses the common identity to convert between logarithmic bases:

logx(z) = logm(z) / logm(x)

By multiplying both sides by log_m(x), you get:

logm(z) = logx(z) * logm(x)

Which is equivalent to the answer in the question you site.

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