(In reply to computer exploration (spoiler)
Seeking to find the exact point where the LHS reaches its maximum, I found it easier to differentiate its logarithm, which is y = ln(x)*0.4^x.
y'=.4^x *(1/x + ln(0.4)*ln(x))
This could be solved iteratively through:
x = 1.1
x = EXP(1 / (x * LOG(5 / 2)))
PRINT x, x ^ (.4 ^ x)
which finds the LHS equal to approximate 1.119625892520564 when x is approximately 1.820921921969026.
Posted by Charlie
on 2008-03-10 17:42:56