So, I am going into college as a math major with a concentration in secondary education, but despite how much I’ve learnt and understood, the one thing I’ve never been able to wrap my head around is logarithms and how they work, what they do, and things such as that. Anyone know a good way to explain it?
Extraneous questions:
what is *ln*?
What does a subscript after the log mean, especially if it’s not 10?
In: 0
Almost every math function has an inverse, or a second function that can undo the first one. Addition and subtraction, multiplication and division, exponents of a variable and roots. This is how we can solve for an unknown variable when we know the result in an equation. But what about exponents *with* a variable (10^x instead of x^10)? That’s what a logarithm is for, to be the inverse of exponents with a variable.
We know 100 is 10^2, so log(10) of 100 is 2. Similarly, log(10) of 1000 is 3. If something grows at 10 times itself each day, the logarithm will describe how many days it would take to get there from 1. But chances are that something real doesn’t suddenly multiply at the end of the day. If we want to know when and during which day it reaches 200, we can put 200 into log(10) and we [get about 2.3](https://www.wolframalpha.com/input?i=log10+200). It would take 2 days and about 7.2 hours to go from 1 to 200 in this situation.
log(10) is different than just log because different logarithms are for different bases. log(10) is for 10^x, log(2) is for 2^x, and the specially named ln (stands for natural logarithm) is for *e*^x.
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