My analytical skills are pretty good but, my math has always been pretty poor. Sometimes I think maybe it's the way it's taught. I was aware of logarithms but, was balled up in definitions and such from math classes.
Here's where the clarity of logarithms came into focus for me and maybe it will be of help to others.
About the time the scientific pocket calculator came out, I was futzing around and had an idea to try. I know that squaring a number is multiplying it times itself and that when the number is 10, raising it to a power gives a number with the same number of zeros as the exponent used (10 to the 6th = 1,000,000) but, what would happen if I tried to make that exponent something other than a whole number? I was expecting an error if I raised 10 to say, the 2.35 power.
To my surprise, instead of an error, I got a number. What's more, it was between 100 and 1000. At that point I must have had an epiphany because I wondered what would happen if I put my result into the log10 thingie. Of course (though it wasn't so obvious to me then), I got back my original numver of 2.35.
I instantly "got it". A logarithm is simply the exponent of 10 with the whole number defining the range (between 100 and 1000 in my example) and the decimal part defining the actual numeric value.
Thinkng I must have stumbled into something so obvious it was common knowledge, I showed it to another technician (not an engineer) and his exact response was, "Is that all there is to it?". Even to this day, I keep expecting that there MUST be more to it than that but, I'll be darned if I can figure out what it may be.
Later, I found out that those are called, "common logarithms" and there are others, especially the natural logarithms. But, they all made a lot more sense once I discovered just what they are.
Here's where the clarity of logarithms came into focus for me and maybe it will be of help to others.
About the time the scientific pocket calculator came out, I was futzing around and had an idea to try. I know that squaring a number is multiplying it times itself and that when the number is 10, raising it to a power gives a number with the same number of zeros as the exponent used (10 to the 6th = 1,000,000) but, what would happen if I tried to make that exponent something other than a whole number? I was expecting an error if I raised 10 to say, the 2.35 power.
To my surprise, instead of an error, I got a number. What's more, it was between 100 and 1000. At that point I must have had an epiphany because I wondered what would happen if I put my result into the log10 thingie. Of course (though it wasn't so obvious to me then), I got back my original numver of 2.35.
I instantly "got it". A logarithm is simply the exponent of 10 with the whole number defining the range (between 100 and 1000 in my example) and the decimal part defining the actual numeric value.
Thinkng I must have stumbled into something so obvious it was common knowledge, I showed it to another technician (not an engineer) and his exact response was, "Is that all there is to it?". Even to this day, I keep expecting that there MUST be more to it than that but, I'll be darned if I can figure out what it may be.
Later, I found out that those are called, "common logarithms" and there are others, especially the natural logarithms. But, they all made a lot more sense once I discovered just what they are.