Independent study on Logarithms

TheShapeOfTime
I'm in grade 11 and I have to do an independent study on Logarithms. I need a problem or puzzle that I will solve after learning logarithms. I was wondering if someone had an example of a really good use of logarithms (i.e. something made a lot easy by the use of logarithms).
 
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You might investigate a piece of antiquity called a slide rule.
 
I strongly second Integral's suggestion!

- Warren
 
Integral said:
You might investigate a piece of antiquity called a slide rule.

Ahh, that looks cool! Thanks!
 
Try rocket science! Calculate the speed acquired by a rocket whose mass varies as it burns up fuel.
 
Tide said:
Try rocket science! Calculate the speed acquired by a rocket whose mass varies as it burns up fuel.

An interesting idea. I shall look into this as well.
 
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Fermat's Last Theorem has long been one of the most famous mathematical problems, and is now one of the most famous theorems. It simply states that the equation $$ a^n+b^n=c^n $$ has no solutions with positive integers if ##n>2.## It was named after Pierre de Fermat (1607-1665). The problem itself stems from the book Arithmetica by Diophantus of Alexandria. It gained popularity because Fermat noted in his copy "Cubum autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos, et...
I'm interested to know whether the equation $$1 = 2 - \frac{1}{2 - \frac{1}{2 - \cdots}}$$ is true or not. It can be shown easily that if the continued fraction converges, it cannot converge to anything else than 1. It seems that if the continued fraction converges, the convergence is very slow. The apparent slowness of the convergence makes it difficult to estimate the presence of true convergence numerically. At the moment I don't know whether this converges or not.

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