Compressing Logs Posted on October 4, 2011 by Mr. Chase Love this. [Hat tip: Tim Chase] Share this:EmailTweetLike this:Like Loading... Related
Reminds me of one of my pet peeves: problems that begin “simplify the following expression.” I say simplify for what purpose? 7/14 simplifies to 50% if one is asking about discounts. Factoring can be simplifying if one is discovering zeros of polynomials. Multiplying a product of polynomials out can be simplifying if one is using Descarte’s rule of signs to discover how many zeros there are. Writing a rational function as a sum of rational functions (as in finding “partial fractions”) simplifies integration.
But taking the joke on its own terms, adding a .ZIP extension doesn’t compress anything. Executing pkzip might.
c:> pkzip “log |x| + log |x+2|”
for example. But that leads to another pet peeve: (We curmudgeons have many peeves.) quotations marks that “are” misused, as in the present sentence with too many. Like lion has 4 letters, in the present sentence with too few. The former even has its own blog page: http://www.unnecessaryquotes.com/
Yes, I completely agree. “Simplify” is *so* problematic.
When is a log expression like the one above ‘simplified’? Is a factored expression simpler than an expanded one? Is an exponential expression simplified with or without negative exponents?
This confusion results in teachers (like me) having to include directions like, “simplify, leaving no negative exponents” or the like. Occasionally there are better, slicker ways to ask the question that still drives home the same point. But I’ll probably always have questions with slightly unclear directions.
This previous blog post relates, somewhat: https://mrchasemath.wordpress.com/2011/02/23/teaching-domain-and-range-incorrectly/
This is where those who propose JIT teaching have a point. Just-in-time teaching teaches a concept when it is needed. We already do that somewhat. Who teaches partial fractions in Algebra? Most teachers wait until Integral Calculus. We could teach simplifying
(*) log |x| + log |x+1| in the context of solving an equation, like setting (*) = 25 and asking to solve for x. So I don’t mean teaching math from an applications-first point of view.
There’s no harm in saying “write the following expressions without any parentheses” or “as a single logarithm.” There is no harm in saying “write this rational function as a polynomial and state the domain on which the polynomial agrees with the rational function.”
Of course words like “factoring” are unambiguous.
At least if you don’t have the wag who says, “x^2 -4 factors into the product of -1 and 4-x^2.”