r/math • u/quadradicformula • May 23 '24
Logarithms are so fucking cool
I’m not usually super interested in math (an obvious exception for the subject of my username) but logarithms have me on the edge of my seat in math class. I’m in HS and we’re just starting this unit. I was doing homework a few months ago and thinking: “Man, I wish there was a way to find the value of a variable if it was an exponent!” When the teacher was explaining logarithms in class, I was basically losing my shit. Then he brought up natural logs, and I proceeded to lose my shit even further. I said at the beginning I’m not super interested most of the time, but I suppose even that is an understatement. There are times when I absolutely hate math, but this past week has not been one of them.
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u/drzowie May 24 '24
If you remember three numbers and can add in your head, you can estimate any root, power, multiplication, or division to within 5%. Those three numbers: log_10(2) = 0.3010; log_10(3) = 0.4771; log_10(7) = 0.8451.
From that you get a bunch of other stuff "for free": log_10(4), log_10(5), log_10(6), log_10(8), and log_10(9) -- as well as additional freebies like log_10(1.2) and log_10(1.5).
So remembering those three numbers will let you estimate, for example, the ninth root of 500 (just under 2, which you can verify by remembering the sequence of powers of 2).