Norman:
When I was taught the exponential functions I was taught that the inverse
exponential was a part of that class. That is, logarithmic functions are
correctly generally referred to as "exponential" or--perhaps somewhat more
accurately--as "inverse exponentials".
I deduce that you disagree and instead think that logarithmic functions are
not part of the class of exponential functions.
That is not my understanding.
Bill
On Monday, September 5, 2016, Norman Yarvin <yarvin@xxxxxxxxxxxx> wrote:
On Mon, Sep 05, 2016 at 07:10:08AM -0400, William Claybaugh wrote:
Norm:
A logarithm is an exponential function.
Not when you're talking about an "exponential effect", it isn't. An
exponential effect is a big effect that grows strongly as you increase
the factor in question; a logarithmic effect is a wimpy one that gets
ever-wimpier as the factor in question increases. In particular,
here, a 10% increase in Isp buys you a 10% increase in delta-v,
whereas a 10% increase in m_initial/m_final buys you less, at least
for launcher-like values of that ratio. (If, say, it starts out as
10, a 10% increase buys you about 4% more delta-v; or if it starts out
as 5, a 10% increase buys you 5.6% more delta-v.)
