Question 558185: I tried to do this but I find it so confusing. Can someone help me?
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 rapaljer(4671)   (Show Source):
You can put this solution on YOUR website! For 16 elements, it would be  steps.
For 512 elements, it would be  steps.
Knowing that ln 2 ≈ 0.693, you can use the law of logarithms to calculate
For additional help with this, please see my own FREE website. To go to my website, use the easy-to-spell and easy-to-remember link www.mathinlivingcolor.com. At the very bottom of this page, there is a link that will take you to my Homepage.
I have a LOT of resources about LOGARITHMS on my website. Once you are on my Homepage, look for the link "Basic, Intermediate, and College Algebra: One Step at a Time." Choose "College Algebra", and look in Chapter 4 for a complete, non-traditional explanation that my own students, before I retired, found a lot easier to understand than the published textbooks of that day. You should really like my MATH IN LIVING COLOR pages, where the most difficult problems are solved IN COLOR. In addition, I have two videos of me teaching the entire chapter on logarithms before I retired. To find my video, look on my Homepage for the link "Rapalje Videos in Living Color."
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Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus
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