I can probably construct a log trendline with an uptrend as long as it is up at all if I use another number base

But yeah the traditional log10 chart line which we were so proud of is now practically broken... I admit that.

There isn't a mathematical difference between bases, unless you use a complex one (in which negative values could be in theory selected, preserving an uptrend by flipping the graph). To understand this better, realize that b

^{mn} = (b

^{m})

^{n}.

So the conclusion to this nonsense is: Bitcoin doesn't die unless it dies, you have your answer now stop trolling (please)

The article you linked actually clearly argues the same thing as I. The section which emphasis my point is in the article you mentioned

http://en.wikipedia.org/wiki/Logarithmic_scale#MotivationHere is the quote in question:

Due to the identity:

log_{b} a = log_{c} a / log_{c} b

the logarithms of any given number a to two different bases (here b and c) differ only by the constant factor log_{c} b.