How can I prove by using the Order notation definition that we can conventionally refer to an algorithm taking "log time", without referring to a particular logarithmic base?
2026-04-05 12:48:13.1775393293
Omitting the refference to a particular logarithmic base - order notation
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Since $\log_an=(\lg_ab)(\log_bn)$, you have that $\log_an$ is just a constant multiple of $\log_bn$, and we know that constant multiples are invisible to asymptotic estimates.