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

Algebra ->  Functions -> 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      Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!
Starting with:
Log%5B2%5D%28n%29 Substitute n = 16.
Log%5B2%5D%2816%29+=+Log%5B2%5D%282%5E4%29 Apply the power rule for logarithms:
Log%5B2%5D%282%5E4%29+=+4Log%5B2%5D%282%29 Recognising that Log%5Bb%5D%28b%29+=+1 we have:
Log%5B2%5D%2816%29+=+4
Similarly for n = 512 (512+=+2%5E9) so...
Log%28512%29+=+Log%5B2%5D%282%5E9%29 and...
Log%5B2%5D%282%5E9%29+=+9Log%5B2%5D%282%29 = 9
----------------------------------------
Ln%288%29+=+Ln%282%5E3%29=3Ln%282%29+=+3%280.693%29=2.079