A Super Nice Exponential Equation

[@bodybuildhistory5004]

very funny, your math tricks make me laugh !

[@Aladin-tp1]

5:45 bro that this mean that : 1/2 = 1/4 ???

[@ShortsOfSyber]

No! (1/4)^(1/4) = (1/2)^(1/2) but 1/4 does not equal 1/2

[@ralphtrucksess7008]

@@ShortsOfSyber but @3:48 you write:
If a^a = b^b --> a=b
that would mean: 1/2 = 1/4

[@musicsubicandcebu1774]

Spencer's Academy just posted the same problem. That's one day later. It was claimed to be an Olympiad problem.

[@ViaanHossain]

I was just putting the x values from minus infinite to plus infinite with the fractions. (Before watching the video). And I found 1/8 or 0.125 for answer but I couldn't solve because I forgot the one to one correspondent rule.thanks

[@اسماعیلخسروی-خ6ظ]

عالی❤❤❤❤

[@barakathaider6333]

👍

[@walterwen2975]

A Super Nice Exponential Equation: (1/x)ˣ = 4ˣ⁺¹⸍¹⁶; x =?
4ˣ > 0; [(1/x)ˣ]/4ˣ = (4ˣ⁺¹⸍¹⁶)/4ˣ, 1/[(xˣ)(4ˣ)] = [(4¹⸍¹⁶)(4ˣ)]/4ˣ, 1/(4xˣ) = 4¹⸍¹⁶
4¹⸍¹⁶ = [1/(1/4)]¹⸍¹⁶ = 1/{[4(1/16)]¹⸍¹⁶} or 4¹⸍¹⁶ = 2¹⸍⁸ = 1/[(1/2)¹⸍⁸] = 1/{[4(1/8)]¹⸍⁸}
1/(4xˣ) = 1/{[4(1/16)]¹⸍¹⁶}; x = 1/16 or 1/(4xˣ) = 1/{[4(1/8)]¹⸍⁸}; x = 1/8
Answer check:
x = 1/16: (1/x)ˣ = (16)¹⸍¹⁶ = 2¹⸍⁴, 4ˣ⁺¹⸍¹⁶ = 4¹⸍¹⁶⁺¹⸍¹⁶ = 4¹⸍⁸ = 2¹⸍⁴; Confirmed
x = 1/8: (1/x)ˣ = [1/(1/8)]¹⸍⁸ = 8¹⸍⁸ = 2³⸍⁸, 4ˣ⁺¹⸍¹⁶ = 4¹⸍⁸⁺¹⸍¹⁶ = 4³⸍¹⁶ = 2³⸍⁸; Confirmed
Final answer:
x = 1/16 or x = 1/8

[@SidneiMV]

(4x)ˣ = (1/4)^(1/16)
(4x)⁴ˣ= (1/4)^(1/4)
4x = 1/4 => *x = 1/16*
but (1/4)^(1/4) = (1/2)^(2/4) = (1/2)^(1/2)
so (4x)⁴ˣ = (1/2)^(1/2)
4x = 1/2 => *x = 1/8*

[@pspprabhat]

X^-x=(4^×)(4^-16)
=>(×/4)^-×=(16/4)^-16
=>×=16