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In general we say that polynomials grow faster than linear functions. but take the following functions, we have that log^3(n) = o(n). here the linear term grows much faster. however, when we increase the power we get the opposite, e. g. n = o(log^7( where the log term grows faster. how can i determine where the limit lies (or where the equality shifts) for such cases? are there general guidelines to follow?

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