I just got introduced to logarithms and natural logarithms (I've been learning this Precalculus stuff by myself) and it all seems very confusing to me.
Logs are a simple way to find the power the base of an exponent is raised by to get the answer, for example, everyone knows that $2^3=8$ (right?), so the log of that would be $\log_2(8)=3$ because $2$ raised to the third power gives $8$.
And the same is to natural logs. Natural log (or $\ln$) is just a "compressed" way of saying $\log_e$. So since $e^1=e$, $\ln(e)=1$.
Question: Is there an easy way to memorize the places where you write the power, and the outcome?
Or, we have:
If $$b^a=c$$ then $$\log_b(c)=a$$
I'm just wondering if there's an easy way to memorize that, because remembering where I put the powers is the difficult part for me.
Also, just a quick little question, you don't have to answer this.
- Why is Natural Logarithm denoted as $\ln$? The "l" is first, so shouldn't it be "Logarithm natural"?