Question

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

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

Answer 1

`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!