A Nice Algebra Problem | Math Olympiad | Exponential Equation

[@sissokosalia4423]

EXCELLENT

[@SALogics]

Thank you so much!❤

[@gelbkehlchen]

Solution:
x^x = 4^(4+x) |/4^x ⟹
(x/4)^x = 4^4 = 2^(2*4) = 2^8 = (8/4)^8 | ⟹ x = 8, because the same operations are done with x on the left side of the equation as with 8 on the right side of the equation.

[@SALogics]

Very nice! ❤

[@SidneiMV]

xˣ = 4⁴4ˣ
(x/4)ˣ = 4⁴
(x/4)^(x/4) = 4 = 2²
x/4 = 2 => *x = 8*

[@SALogics]

Very nice! ❤

[@ChavoMysterio]

nⁿ=4^(4+n)
nⁿ=4⁴•4ⁿ
(¼n)ⁿ=4⁴
[(¼n)ⁿ]^¼=(4⁴)^¼
(¼n)^(¼n)=4
(¼n)^(¼n)=2²
¼n=2
n=8 ❤

[@SALogics]

Very nice! ❤

[@trojanleo123]

x = 8

[@SALogics]

Yes, you are right! ❤

[@walterwen2975]

Math Olympiad: xˣ = 4⁴⁺ˣ; x =?
xˣ = 4⁴⁺ˣ = (4⁴)(4ˣ), 4ˣ > 0, (xˣ)/(4ˣ) = 4⁴ = 2⁸ = (8/4)⁸, (x/4)ˣ = (8/4)⁸, x = 8

[@SALogics]

Very nice! ❤