I mean, I’ve used them in algebra many times but I never really understood what it does. Kinda like in biostatistics how I could do the math, but how it worked was beyond me entirely.
So yeah: like what’s this sorcery and what does it do/why do we use it?
In: Mathematics
You know how exponents work, right? Some number taken to a power (call it “n”)is the same as multiplying the number by itself n times.
A^2 = A x A
A^3 = A x A x A
A^4 = A x A x A x A
But what if the exponent (2, 3, 4, etc.) could be a non-integer like 2.6 or 3.524? That exponent is the logarithm.
You can express any number like this.
10^2.65 = 446.68
In this example 2.65 is the Base10 logarithm of 446.68
Here’s the real beauty of logarithms: adding logarithms is the same as multiplying the numbers.
10^2.65 = 446.68
10^1.37 = 23.44
What happens if you multiply 446.68 x 23.44? The answer is 10,470
What happens if you add 2.65 + 1.37?
The answer is 4.02
10^4.02 just happens to be 10,470.
In fields like radio frequency (RF) engineering, we use this property all the time. We just multiply the logarithm by 10 and call it “dB” units. This way you can add logarithms all day long, and it’s the same as multiplying the numbers. Adding is much easier than multiplying!
Fun fact: the fret spacing on a guitar fingerboard is logarithmic.
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