What is an effective and practical means to teach about natural logarithms and log laws to high school students? My students are quite practically minded, and I have found that teaching them concepts in a practical manner to be very helpful (maths 'experiments'; modelling on the smartboard etc). 
I am looking for a practical means (hands on preferably) to teach about the log laws of natural logarithms.
 A: For introducing logarithm, perhaps something like starting with exponential population growth and then noting that the graph is linear in log-space?
You can then change back and forth between representations and see how things like base-change affect the plot and the interpretation.
This is also probably representative of where less-mathematical scientists run into logarithms the most.
A: I would start with the historical reason:
It is hard to multiply with pencil and paper.
From this, it is natural to
try to find a method of multiplying by adding.
For this,
you need a function $f$
such that
$f(xy) = f(x)+f(y)$
and a method of getting
$z$ from $f(z)$.
One place where this occurs
is "number of zeros after the one"
in powers of ten (or two if you like binary).
If $n = 10^j$,
$m = 10^k$,
and $f(n) = j$ and $f(m) = k$,
then $f(nm) = j+k$.
So "number of zeros" works for powers of ten.
Then, what about when $n$ is not a power of ten?
Turn this around, and ask
"what does $f(n) = 1/2$ mean?"
If $f(n) = 1/2$, and we want the rule
$f(xy) = f(x)+f(y)$ to hold,
then 
$f(n^2) = f(n)+f(n)
=1/2+1/2 = 1$,
and since $f(10) = 1$,
$n^2 = 10$ or
$n = \sqrt{10}$.
Continuing this,
we get the usual
"if $f(n) = r$ where $r$ is rational,
then $n = 10^r$".
Eventually, you get logs and tables
and inverse logs
and slide rules,
and here we are.
