SOLUTION: Part V: Logarithms 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

Question 623398: Part V: Logarithms
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.
Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
Starting with:
Substitute n = 16.
Apply the power rule for logarithms:
Recognising that we have:

Similarly for n = 512 () so...
and...
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