The astrologer William Lilly (1602-1581) recounted a famous meeting:
Henry Briggs, a math professor from London, traveled up to Scotland to meet Napier. When introduced, the two stood looking at each other in silent admiration for a quarter of an hour before Briggs said, “My lord, I have undertaken this long journey purposely to see your person, and to know by what engine of with or ingenuity you came first to think of this most excellent help in astronomy, viz. the logarithms; but, my lord, being by you found out, I wonder nobody found it before, when now known it is so easy.”
One activity that I’ve used to teach logarithms — which former students who became secondary teachers have used to teach logarithms to *their* students — involves telling students that log_10 2 = 0.301 and log_10 3 = 0.477 (approximately) and then asking them to use the laws of logarithms to find as many other logarithms of integers as they can. For example, after they find that log_10 6 = log_10 2 + log_10 3 = 0.301 + 0.477 = 0.778, they can check with their calculators and verify that, whaddaya know, it actually worked.
I’ve always found that part of the problem is that this is one of the first times [unless students have done basic trig functions] that students encounter a word “log” that is supposed to be an operation. Most of the operations they are used to at this point have been abstracted into symbols: + – * / with the minor exceptions of maybe fractional powers (roots) and parentheses involving more than one symbol. This kind of thing crops up elsewhere, but I try to ease them into the new symbol and not worry about bases too early. It brings the intimidation factor down quite a bit.
Some people still have to use the log tables. Like 11th grade students in India(coz calculators aren’t allowed in the exams). But it makes it all the more confusing coz you tend to mess up the mantissa and exponent parts.
Wow u make it so simple to understand the logic behind logarithms….wish we were explained this in school 🙂
But nevertheless better late than never….thank you 🙂
Well those logs are so true. Seemed a little to easy considering i hate math. But log(s) a + b = ?. Duh lol. Plus Xtremly, would +hY. It in a heart beat. Me.
Awesome! Why did no one tell me that when I actually needed to use them??
Even better with a slide rule. (what’s that?)
Yes, why skip over that bit of history?
The astrologer William Lilly (1602-1581) recounted a famous meeting:
Henry Briggs, a math professor from London, traveled up to Scotland to meet Napier. When introduced, the two stood looking at each other in silent admiration for a quarter of an hour before Briggs said, “My lord, I have undertaken this long journey purposely to see your person, and to know by what engine of with or ingenuity you came first to think of this most excellent help in astronomy, viz. the logarithms; but, my lord, being by you found out, I wonder nobody found it before, when now known it is so easy.”
– from e: The Story of a Number by Eli Maor
One activity that I’ve used to teach logarithms — which former students who became secondary teachers have used to teach logarithms to *their* students — involves telling students that log_10 2 = 0.301 and log_10 3 = 0.477 (approximately) and then asking them to use the laws of logarithms to find as many other logarithms of integers as they can. For example, after they find that log_10 6 = log_10 2 + log_10 3 = 0.301 + 0.477 = 0.778, they can check with their calculators and verify that, whaddaya know, it actually worked.
More details can be found here: https://meangreenmath.com/2013/08/09/square-roots-without-a-calculator-part-9/
I’ve always found that part of the problem is that this is one of the first times [unless students have done basic trig functions] that students encounter a word “log” that is supposed to be an operation. Most of the operations they are used to at this point have been abstracted into symbols: + – * / with the minor exceptions of maybe fractional powers (roots) and parentheses involving more than one symbol. This kind of thing crops up elsewhere, but I try to ease them into the new symbol and not worry about bases too early. It brings the intimidation factor down quite a bit.
Of course the inverse of log(x) is exp(x), but so much for computer programming (coding if you wish)
*Click*
That’s the sound of logarithms making sense in my head.
Some people still have to use the log tables. Like 11th grade students in India(coz calculators aren’t allowed in the exams). But it makes it all the more confusing coz you tend to mess up the mantissa and exponent parts.
Logarithms are a group isomorphism from (R+, x) –> (R, +)
I really like Vi Hart’s video on the subject.
https://www.youtube.com/watch?v=N-7tcTIrers
And, when I learned to fly, I found out that pilots still use slide rules. The E6B flight computer.
https://en.wikipedia.org/wiki/E6B
It does logarithms of the front and Trigonometry on the back.
The logarithm *is* the exponent.
Wow u make it so simple to understand the logic behind logarithms….wish we were explained this in school 🙂
But nevertheless better late than never….thank you 🙂
:’-(
Well those logs are so true. Seemed a little to easy considering i hate math. But log(s) a + b = ?. Duh lol. Plus Xtremly, would +hY. It in a heart beat. Me.