I already know the value of y, can you help me to find T? thanks :)

y=-ln(-ln((T-1)/T))

1 Answer
Nov 23, 2017

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

Explanation:

Okay, let's solve this step by step.

y=−ln(−ln((T−1)/T))

-y=ln(-ln((T-1)/T))

To make things simpler, let's set a=-ln((T-1)/T)

-y=ln(a)

This equation basically means:

e^-y=a

Let's continue:

e^-y=-ln((T-1)/T)

-e^-y=ln((T-1)/T)

Once again, we can set a variable for (T-1)/T and get rid of the logarithm. Eventually, we will get:

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

T*e^(-e^-y)=T-1

1=T-T*e^(-e^-y)

T(1-e^(-e^-y))=1

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

Since you know y, you can solve for T. If you see any mistakes, just comment. Hope this helps!