Solving a 'Harvard' University entrance exam question

Added: 2026-06-02

[00:00:00]Hello Friends find the value of 't' If t^t=7^2 let's have a solution this question is same as t^t=49 since 7^2=7x7=49 take natural log 'ln' on both sides lnt^t=ln49 since lna^b=blna then It will be tlnt=ln49 apply here Lambert W function which is W(a.e^a)=a like If we have 2.e^2 W(2.e^2)=2 I hope you understood so tlnt=ln49 can be written as e^lnt.lnt=ln49 as t=e^lnt solve this It can be written as lnt.e^lnt=ln49 which is like 'a.e^a' so apply Lambert W function on both sides W(lnt.e^lnt)=W(ln49) W(a.e^a)=a It will be W(lnt.e^lnt)=lnt I hope you understood lnt=W(ln49) to find the value of 't' we have to take here base 'e' on both sides e^lnt=e^W(ln49) e^lnt=t so It will be t is approximately equal to 3.278 which is our the value of 't' thanks for watching this video please subscribe this channel to get the notification of my new videos and don't forget to share these videos with your classmates and friends so that they also have a benefit of it ok bye