How do we calculate unknown in such problem as this: 0.78=1*(1\2)^(t/100000)

Take the log of both sides.
Log(0.78) = Log(.5^(t/1000000))
Now you can use the log property : Log(a^b) = bLog(a)

which gives, Log(0.78) = (t/1000000)log(.5)
(Log(0.78)-Log(.5) )1000000 = t

t = 35845.4