Here's two that I really enjoyed. This first one looks like a real doozy without a calculator, but lots of stuff cancels. Classic problem that demonstrates the spirit of the UVM Math Contest.

"Simple" logarithms.

Difficulty: easy.

Difficulty: Easy, but my students got all wrapped up in it. Don't know why..

Standard instructions for this series: No calculator allowed. Express answers in reduced form. Rationalize denominators. Radicals must be reduced. All numbers are base ten unless otherwise specified. Do not approximate radicals or π. Leave such answers as 1025π or √39, for example. Source: UVM Math Contest 2013

answer 03, answer 04.

Thanks. Used the log question in class on Friday... we covered the relevant material a week earlier... problem made a nice diversion.

ReplyDeleteInteresting, tangential discussion on converting log base 8 of x into log base 2 of something.