One important application of logarithms is found in various computer search rout

Question

One important application of logarithms is found in various computer search routines. For example, a binary search algorithm on a table (or array) of data takes a maximum of log2n (“log base 2, of n”) steps to complete, where n is the number of data elements that can be searched. How many steps (at most) are needed for a search of a table with 16 elements? 512 elements? Explain.
The approximation of the natural logarithm of 2: ln 2 ˜ 0.693 is commonly used by applied scientists, biologists, chemists, and computer scientists. For example, chemists use it to compute the half-life of decaying substances. Based on this approximation and the power rule for logarithmic expressions, how could you approximate ln 8, without a calculator? Explain.

Explanation / Answer

with 16 elements

total time = log2 16 = log2 2^4 =4* log 2 2 = 4*1 = 4

with 512 elements

total time = log2 512 = log2 2^9 =9* log 2 2 = 9*1 = 9

ln2 = 0.693

ln8 = ln2^3 = 3 ln2 = 3 *0.693 = 2.079

those above are based on logarithmaic properties.

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