I got this asked as a High School interview question and I was CONFUSED

[@RealQinnMalloryu4]

{5x+5x ➖ }=10x^2 5^5x^2 2^3^2^3x^2 1^1^1^3x^2 3x^2 (x ➖ 3x+2).

[@alfredsteele979]

You shouldn't complain. If it weren't for videos like this I wouldn't have learned about the Lambert function. Also, please note that at the end he showed why the answer was complex. The grafs didn't intersect

[@florisv559]

I was offering constructive criticism. What's wrong with that? I'd say that people who still need such an expanded reduction of the original equation to the Lambert W function because they aren't comfortable with logarithms etc. yet, shouldn't start with the Lambert W function but should first get comfortable with logs.

[@florisv559]

You first spoon feed the viewer with simple steps to solve the equation, then you start about the Lambert W function, which is indeed higher maths, then you loosely comment that the equation doesn't have any real solutions, without showing how you come to that conclusion. Try to be more consistent and your videos will improve greatly.

[@TimBoulette]

Ask for your money back.

[@janami-dharmam]

how do you know that W(-ln5) does not exist?

[@florisv559]

@@janami-dharmam Like this: f(w) = we^w for real w has an absolute minimum -1/e for w = -1. -ln(5) < -1 < -1/e, so we^w can't get that value. Another way to see it is to view the graphs of the functions x-> x and x -> 5^x - they don't intersect.

[@Snow41174]

@@florisv559 He referred to a previous video where he discussed the relationship of complex valued solutions and non-intersecting graphs. BUT WHICH VIDEO?

[@RAMPRASADLANDAGE]

Make videos on SAT maths questions (vote button)

[@Snow41174]

You referred to a previous video where you discussed the relationship of complex valued solutions and non-intersecting graphs. BUT WHICH VIDEO?

[@tzirvee]

5^log x = x ⁵

[@randyparker5721]

5^0=0 X=0

[@fubaralakbar6800]

Any number to the 0 power = 1

[@hamzahaidar2084]

No. X⁰ = 1 ( X€ R) And 5^x≠x (X€R) So the solution is complex/ imaginary

[@Mack-ed1ig]

You are solving questions for other people to see not for yourself. For God's sake, writing should be bigger so we can see easily .

[@БоянБожанов-м1н]

Its written pretty well. Have you checked your eyes recently

[@edwardhuff4727]

x = -0.01075 - 0.98279 i

[@edwardhuff4727]

5^x = x (e^ln 5)^x = x e^(x ln 5) = x x ln 5 = ln x (ln x)/x = ln 5 (ln x)/(e^ln x) = ln 5 (ln x)e^(-ln x) = ln 5 (-ln x)e^(-ln x) = -ln 5 W((-ln x)e^(-ln x)) = W(-ln 5) -ln x = W(-ln 5) ln x = -W(-ln 5) x = e^(-W(-ln 5))

[@janami-dharmam]

how??

[@edwardhuff4727]

​​@@janami-dharmamWolfram Alpha or Mathematica, or one of many other computer algebra systems. Look at Wikipedia article on CAS.

[@edwardhuff4727]

Here's more solutions. There are countably many. Sheet refers to the Riemann surface, which is cut into sheets. Each sheet fills the complex plane. All of the complex x values satisfy 5^x=x. sheet=-5 x=1.7462696339565527+16.5264299576489i x-5^x=10^-14 + 0.i sheet=-4 x=1.5796262962043934+12.610451070467139i x-5^x=10^-14 - 10^-15i sheet=-3 x=1.3507162537895936+8.688085376179854i x-5^x=10^-15 - 10^-15i sheet=-2 x=0.9815502377624126+4.753430109599094i x-5^x=10^-16+10^-16i sheet=-1 x=-0.010750838472555747+0.9827872262285992i x-5^x=-10^-17+0.i sheet=0 x=-0.010750838472555783-0.9827872262285992i x-5^x=10^-17+0.i sheet=1 x=0.9815502377624126-4.753430109599094i x-5^x=10^-16-10^-16i sheet=2 x=1.3507162537895936-8.688085376179854i x-5^x=10^-15+10^-15i sheet=3 x=1.5796262962043934-12.610451070467139i x-5^x=10^-14+10^-15i sheet=4 x=1.7462696339565527-16.5264299576489i x-5^x=10^-14+0.i sheet=5 x=1.8774508360596127-20.43888917162955i x-5^x=10^-14+10^-15i