Wednesday, September 8, 2010

When FLG Felt Dumb

Recently, FLG was working on a binomial distribution problem. To make a long story short, he had to solve this equation for an unknown variable:

The only unknown happened to be the n, which as you can see is in the exponent.  FLG sat there for about three minutes, scratching his head, trying to remember how to get the damn variable out of the exponent.  Eventually, he just fucking google'd it. 

He didn't have to click on any of the links.  One of the previews said something about logarithms, and FLG remembered that if you take the natural log of both sides the exponent comes down and it's a multiplication issue.  In hindsight, this all makes perfect sense.  Logs and exponential functions are inverse functions.  It bothers FLG that he couldn't remember this straight away.


Andrew Stevens said...

It's not so dumb. I work with equations like that virtually every day so it's not possible for me to forget that particular technique, but it's perfectly understandable for someone who doesn't deal in mathematics for a living. I don't think it's immediately intuitive even if you know that exponents and logarithms are inverse functions.

I'm always a bit bemused when I'm explaining mathematical problems to people how often non-mathematicians are quite comfortable with exponents, but are intimidated or completely clueless about logarithms. As you say, they're inverse functions, so understanding exponents should make logarithms completely comprehensible in theory. But in practice it seems to be another story.

FLG said...

I think most people understand exponents so well solely because of lengthy exposure to quadratic equations.

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