Thread: Natural log problem

I am doing a flight control module at university, and maths has never been a strong point of mine.

My problem is:

y(t)=k(1-e^-t/T)

Where y(t)=0.5, k=6/17 and T=1/17

So i can get to this point:

(0.5)17/6 = 1-e^-17t

But obviously if i go any further i am going to have to take natural log of a negative number which obviously cannot be done and i dont know anyway around it.

Any help would be great

Thanks

The supremum of 1 - e^(-t/T) is 1 (see this graph, which approaches 1 very fast because of the large factor of 17). So, the supremum of y(t) is 6/17 < 0.5, which means that there are no solutions.