Logarithmic response of PN junctions

I was just musing about "log amps", where they exploit the
exponential/logarithmic relationship between the current and
voltage of a PN junction.

My question is, is that always "log e", ie., "ln"? My point
being, is it _always_ base "e", rather than, say, log 10, or
log 2, or log something else?

Is that true for silicon, germanium, gallium arsenide, every
semiconductor?

Is that why they're called "natural logs"? If that's true, I
actually find it kind of spooky! :-)

Thanks!
Rich

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