Matt wrote:
On Fri, 19 Feb 2010 16:21:21 -0800 (PST), Andrew Usher wrote:

The very first tables of logarithms were according to the natural base
e (essentially). Base 10 was only adopted because it is somewhat more
easy for calculation with the decimal system.

That seems like a reasonable thing to do.

It was then!

there is no
further reason to use base 10 logarithms at all.

For anything?

For anything, yes.

Yet, many fields of science continue to do so.

If they find it convenient to do so, why not?

Are you proposing that the definition of pH be changed to use natural
logs? For what benefit?

It would remove the factor of log 10 from several equilibrium
equations in that well-known equation (I can't remember the name)
relating concentration and oxidation potential. Actually that's pE,
but pH and pE obviously ought to have the same units. Indeed the best
unit for pH (or pKa) would be Volts.

Sometimes this creates
confusion, as in the fact that optical depths may be measured either
way, and it is not always specified which.

Then they should specify which. Poor expression by some is not a
reason to hamstring everyone else.

Work out the mathematics yourself. If the thickness if x, and the
optical depth A (for attenuation), we should surely have

A = -x dI/dx (I = intensity)

which integrated gives

I/I0 = exp(-A),

proving that base e is the correct way. (If scattering as well as
absorption is significant (which it generally is not) the relation is
complicated, but base e also works there.)

and there is the serious
disadvantages of always having to insert factors of log 10.

"Always" where?

Where do you think? In equations just like the preceding.

Andrew Usher