A very tricky math question with exponents | Can You Solve? 

Input 2^256 = 256^32 Result True Left hand side 2^256 = 115792089237316195423570985008687907853269984665640564039457584007913129639936 Right hand side 256^32 = 115792089237316195423570985008687907853269984665640564039457584007913129639936 Logarithmic form 256 log_2(2) = 32 log_2(256)

assume x= 2 to the power m , so 2^2^m=2^m^32 hence 2^m=m*32 if we put m=8 then 2^8=32*8 which is 256 or 2^2^n=n+5 hence n=3 by considering m=2^n . hence x=2^m=2^8=256

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X=256 final answer

Very nice

I have a question for you What is tan 90° / sec 90° ? I don't know how to solve it but answer is not 'undefined' It is '1', can you solve this ASAP?

Because x is raised to an even power, this equation potentially has three real roots. 2^{-1}0^{32}, so a real root exists between -1 and 0. 2^1>1^{32} and 2^2

2ˣ = x³² (2ᵃ)ˣ = x³²ᵃ x = 2ᵃ = 32a a2⁻ᵃ = 1/32 -a2⁻ᵃ = -1/32 = -(2)⁻⁵ -(2)⁻⁵ = (-2ᵘ)2⁻ᵘ⁻⁵ 2ᵘ = u + 5 => u = 3 -(2)⁻⁵ = -8(2)⁻⁸ -a2⁻ᵃ = -8(2)⁻⁸ -a = -8 => a = 8 x = 2ᵃ => x = 2⁸ = 256

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4 2^2 (x ➖ 2x+2) x^2^16 x^2^4^4 x^2^4^4 x^2^2^2^2^2 x^1^1^1^1^2 x^1^2(x ➖ 2x+1).

2^x = x^32 ln(2^x) = ln(x^32) x*ln(2) = 32*ln|x| ===> two cases 1st case: x > 0 x*ln(2) = 32*ln(x) ln(x)*x^(-1) = ln(2)/32 ln(x)*e^ln(x^(-1)) = ln(2)/32 ln(x)*e^(-ln(x)) = ln(2)/32 -ln(x)*e^(-ln(x)) = -ln(2)/32 W(-ln(x)*e^(-ln(x))) = W(-ln(2)/32) -ln(x) = W(-ln(2)/32) ln(x) = -W(-ln(2)/32) x = e^(-W(-ln(2)/32)) ===> -1/e < -ln(2)/32 < 0 ===> 2 real solutions x₁ = e^(-W₀(-ln(2)/32)) = 1.0223929402057803206527516798494005683768365119132864517728278977... x₂ = e^(-W₋₁(-ln(2)/32)) = 256 2nd case: x < 0 x*ln(2) = 32*ln(-x) ln(-x)*x^(-1) = ln(2)/32 -ln(-x)*x^(-1) = -ln(2)/32 ln(-x)*(-x)^(-1) = -ln(2)/32 ln(-x)*e^ln((-x)^(-1)) = -ln(2)/32 ln(-x)*e^(-ln(-x)) = -ln(2)/32 -ln(-x)*e^(-ln(-x)) = ln(2)/32 W(-ln(-x)*e^(-ln(-x))) = W(ln(2)/32) -ln(-x) = W(ln(2)/32) ln(-x) = -W(ln(2)/32) -x = e^(-W(ln(2)/32)) x = -e^(-W(ln(2)/32)) ===> ln(2)/32 > 0 ===> 1 real solution x₃ = -e^(-W₀(ln(2)/32)) = -0.979016934957784612322582550011650068748090048886011676265377083...

Nice problem! nice solution! ❤❤

r u Castilian? if so i am glad.

Nice

2 to the power root 2 is rational number or irrational number please reply

ln2/2^5 , /*2^3/2^3 , 2^3*ln2/2^8 , 8*ln2*e^(-)8*ln2=lnx*e^(-lnx) , /*(-1) , -8*ln2*e^(-)8*ln2=-lnx*e^(-lnx) , case 1 , -8*ln2=-lnx , ln2^8=lnx , x1=2^8 , x=256 , case 2 , W(-ln2/32)=-lnx*e^(-lnx) , W(-ln2/32)=-0.022145899 , -0.022145899=-lnx , x=e^0.022145899 , x2=1.02239 , test , x1=256 , 2^256=1.15792*10^77 , x1^32=1.15792*10^77 , OK , test , x2=1.02239 , 2^1.02239=2.03129 , 1.02239^32=2.03129 , OK ,

.....JUST DIFF/INTEGRAL AND IT'LL BE faster ........I JUST *hate* LINEAR ALGEBRA

Есть ещё 2 решения: X=1,022393 X= --0,979017

I stopped watching as soon as you copied the equation