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Gear2d
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I was wondering how would I go about proving the Log of a Power Rule:
log(n^k) is O(log(n)) for any constant k > 0
log(n^k) is O(log(n)) for any constant k > 0
mistermath said:You should show what you've tried, but basically..
log (n^k) = k log (n), and use w/e technique you want to show the constant up front does not matter.
OR are you asking how to prove the power rule for logs? I'll give a hint..
log (x) = y <=> 10^y = x
(assuming log has base 10 and <=> means if and only if).
Big Oh Notation is a mathematical notation used in computer science to describe the complexity of algorithms. It represents the maximum amount of time or space required for an algorithm as the input size increases.
Big Oh Notation helps us analyze the performance of algorithms and make informed decisions about which ones to use in different situations. It also allows us to compare the efficiency of different algorithms.
Big Oh Notation is calculated by looking at the number of operations an algorithm performs as the input size increases. The most dominant term is then used to represent the complexity, ignoring any coefficients or lower order terms.
The most common types of Big Oh Notation are O(1) (constant time), O(log n) (logarithmic time), O(n) (linear time), O(n^2) (quadratic time), and O(n!) (factorial time). There are also other variations such as O(n log n) and O(n^3).
Big Oh Notation can be used to analyze and improve the efficiency of algorithms in various applications, such as data sorting, searching, and optimization problems. It can also be used to predict the behavior of software systems as the amount of data they need to process increases.