Decimal ExponentsDate: 03/19/99 at 11:06:39 From: Richard Urich Subject: Decimal Exponents Is there a way to find x^y, where y is a decimal, without the use of a calculator? I know x^(y/z) can be expressed as (x^y)^(1/z), but I cannot figure out how to do a (1/z) exponent without a calculator. It has to be possible if the calculator does it, so I would like to know how calculators do it. Thank you. Date: 03/19/99 at 18:25:38 From: Doctor Rick Subject: Re: Decimal Exponents When I was in school, we did not have calculators, but we could compute x^y. We had another help, though: a logarithm table (or a slide rule, which is a log table on a stick). Somebody spent a lifetime calculating the logarithms, and I could use that person's lifetime work to calculate powers. You can do the same on a calculator without touching the x^y key. For instance, to find 3.14^2.718, you would enter: 3.14 LOG * 2.718 = 10^x getting the answer 22.42099, which is the same answer I get using the x^y key. In math notation, log(x^y) = y * log(x) I do not know, but I assume that calculators use their log function to compute powers. I also do not know for sure how calculators implement the log and exponential functions. There are a number of series expansions that could be used to approximate the log as closely as needed, but I would not be surprised if they use some method incorporating a lookup table. If you want to find out about how calculators do it, you might try an article referenced in this Dr. Math Archives answer: http://mathforum.org/dr.math/problems/kuhn12.3.96.html - Doctor Rick, The Math Forum http://mathforum.org/dr.math/ |
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