I have heard of logarithms, and done very little research at all. From that little bit of research I found out its in algebra 2. Sadly to say, I'm going into 9th grade, but yet I'm learning [calculus!?] and I don't know what a logarithm is! I find it in many places now. I deem it important to know what a logarithm is even though I'm jumping the gun in a sense. My understanding of concepts, is just like that of programming. In the mean time, you know its there, and your ITCHING SO HARD to find out what that is, but nope! For now we use it, tomorrow we learn what it does.
I just know that to identify a logarithm at my level, I just look for a log. 😛
Best Answer
If you know what a power function is:
$$a^b=c$$
you can choose to solve for $a$ or $b$. If you want $a$, take $b$-th root on both sides:
$$a=\sqrt[b]{c}$$
Imagine $b=2$.
However, if you want to get $b$, you take the logarithm:
$$b=\log_{a}c$$
Here, I used the logarithm with a base $a$. Logarithms of different bases are related: they are simple multiples of each other. Common logarithms are $\log_{10}$ (the base is usually skipped), and the natural logarithm ($\log_e x=\ln x$) which is a very nicely-behaved function when you go further in calculus.
The numerical meaning of logarithm can be roughly understood as this: the whole part of the value of $\log_{10} x$ counts the number of digits in $x$. For instance
$$\log 1=0$$ $$\log 10=1$$ $$\log 100=2$$ $$\log 1000=3$$
and so on. Of course, you can evaluate something like $$\log 500=2.69...$$ $$\log 0.05=-1.30...$$
The rest of the properties follow from the definition that it inverts $a^b=c$. For instance, logarithm of a product can be split into sum of logarithms:
$$\log{ab}=\log a + \log b$$
Ultimately, it's just another elementary function, like roots, polynomials and so on.