@YarGnawh
this lambert W function feels like a cheat code.
@aubrey1008
I don't think anyone is learning the Lamber function in high school. Therefore not sure this would be on any college entrance exam.
@Vega1447
There is no Harvard Entrance Exam and no need to reference the Lambert W function. The solution is between 3 and 4. Just take the log of each side : t log t=2log 7. Then use a couple of iterations of Newton's method to solve: t=(t+2*log(7))/(1+log(t)). Solution is approximately 3.278031523596059
@Name-ps9fx
I, lacking any Calculus skills, use the "Artillery" method. T^t = 49 3³ = 27 4⁴ = 256 I have now "bracketed" the range, within which is the target. Now we just increase the minimum range (3) by tenths: 3.2^3.2 = 41.35 3.3^3.3 = 51.42 This is the new bracket, we then adjust our estimations by hundredths: 3.27^3.27 = 48.15 3.28^3.28 = 49.21 We then continue finding each range, and increasing the next decimal until we derive adequate accuracy required by the question. 😊
@jeremybearimy_0
3^3=27 (low) 4^4=256 (high) 3.5^3.5 (high) 3.25^3.25 (low) 3.275^3.275 (low) 3.28^3.28 (high) 3.2775^3.2775 (low).... quickly got to ~3.2781, but could keep going for more accuracy
@sparegod149
My dumbass really thought 7⁷ =49 .
@mrrandom.
Please use ln instead off log as log with no base is used for base 10
@UditPradeep_TOURBILLIONW16
To solve \(T^T = 49\), take natural log on both sides: \(T \ln T = \ln 49\). Since \(\ln 49 ≈ 3.8918\), solve \(T \ln T = 3.8918\). This transcendental equation gives \(T ≈ 3.3\) as the approximate solution. Exact value needs numerical or graphical methods.
@mikeburns6603
There are dozens of videos similar to this where the solution is always the W function. They're trying to make the W function into one of the primary functions, such as ln, exp, sin, cos, etc. But one could always create a problem for which a Jessel function is the solution. If you do it over and over, then you can prtend like Jessel functions should be included in the list of primary functions.
@micahmeneyerji
0:39 4^4 is not 64!
@gauisameme8697
pls use ln() since log is mostly used for 10 asw edit: i read about it more and found out log(x) has many bases including e, 10 and 2 - comp science uses 2 since binary has 2 digits - higher levels of maths / physics mostly use base e - highschool math & chem use base 10 (e.g when calculating pH) and many calculators have log(x) as base 10 tldr; the meaning of log depends on the application/context, but using ln() makes it more clear (esp for high school students)
@MisterJeffy
This would have more value to more people if you explained the basics of the steps you took to solve it.
@fabricer9623
OR you can use the well known Wilson L function, the main property of which is L(x^x) = x. Which yields x = L(49) = 3.278 approximately.
@tschantz
Looking for the W button on my calculator…
@vishalmishra3046
t^t is a continuous, differentiable and monotonically increasing function . Since 3^3 = 27 < 256 < 4^4, therefore 3 < t < 4. Therefore, apply Newton's method to get t = 3.278031523596059366055947260535156966261673645376747543163853771604845412696293875445828810498337202... (100+ places of decimal accuracy with near zero effort). No weird / less-known or one-off or unusual (including Lambert) function required to solve this entire class of problems to any arbitrary desired accuracy. [ How would you calculate Lambert W function anyway ? ]
@Cricketlover-e1y4l
Lambert W Function The Lambert W function, also known as the Omega function, is a mathematical function used to solve equations in which the variable appears both inside and outside of an exponential function or logarithm. Definition The Lambert W function is defined as the inverse function of: f(W) = We^W
@akr1011
t lnt = ln 49 Lnt= 49/t Plot graph, get intersection, simple Ans t= 3.278 -althaf Calicut
@jimmcneal5292
Honestly they should explicitly tell about Lambert W function, using it is quite random, and unless student specifically knows it he'll likely invent some other function(like V=lnW) to solve the equation
@ManishJoshi-o5u
t^t = 49 t.ln(t) = ln(49) t = ln(49)/ ln(t) since 3^3 = 27 and 4^4 = 256, so 3<t<4 use 3 as initial guess. use any numerical method like fixed point iteration method, Nr method etc. to do this with fixed point iteration method save 3 as ans in calculator. type, ln(49)/ln(ans) and repeatedly spam '=' , you will get 3.278..
@Universee_201