Harvard Failed To Solve This | A Challenging Exponential Problem

[@Don.Franco_Film]

How do you "infer" that x > y? And then arrive at x=3, y=4? (your inference is just wrong)

[@maddenbanh8033]

i've tried it algebraically x^y > y^x y*ln(x) > x*ln(y) (take log) ln(x)/x > ln(y)/y (put each part on their sides) from here is a massive stretch tbh -ln(x)/x < -ln(y)/y (multiply -1 inverting the inequality) ln(1/x)/x < ln(1/y)/y (property of logarithms) e^ln(1/x)*ln(1/x) < e^ln(1/y)*ln(1/y) (expand 1/x into exponential) ln(1/x) < ln(1/y) (lambert W function) -ln(1/x) > -ln(1/y) (invert again) ln(x) > ln(y) (property of logs) x > y might be wrong tbh

[@chrisjust7445]

At 1 min, you say x^y > y^x and x > y > 0. How did you get to that conclusion? What if x^y and y^x are both negative? Ex. -17 - (-34) = 17 Also, couldn't there be some complex number solutions also?

[@rifatmithun8948]

First, what are x and y? Are they real numbers, natural numbers, or integers? And for the inference x^y>y^x>0 ==> x>y>0 I think it is only true for x,y in (0,1). There are infinitely many solutions in real numbers. I can think of (18,1) and (1-16) for integers.

[@danielenglish2469]

You just found one solution to the first problem. Another easy solution is x=18, y=1.

[@G7Animated]

Got this answer instantly

[@mariusherghelegiu6241]

as usual in this youtube stuff like that: any equation should be first clarified in which number set is sought. What you tried here was to find solutions in N, whereas you found exactly 1 solution and another comment here mentions also the solution (x,y)=(18,1). Very poor performance.

[@Advay-df8lw]

LOL, I solved this looking at the thumbnail

[@TheCondoInRedondo]

At the 0:58 mark you claim that it is fair to "infer" (your words) that Y must be > 0. Why cannot Y be a negative number, which (when raised to an even exponent) become a positive value, thus satisfying the previous interfence? I get that your claim does turn out to be true. But, I fail to see the logic of your claim at the 58-second mark. How can you know for certain that Y>0 at that point in time? Also, at the 3:45 mark, your rational for factoring 17 is that both A and B are positive integers. How do you know that both A and B are positive integers, which is necessary knowledge to split 17 into 1 and 17 and force the solution to fit into 1 and 17? It seems as if the problem itself must have originally included wording that X and Y are positive integers. Or, does that restriction not need to be the case in order for you to solve the problem using the "inferences" that you did?

[@AbdulJabbar-ce6ix]

Your videos are interesting