A MIND BLOWING Radical Math Problem | Exponential Equations

[@prabhudasmandal6429]

Interesting problem, solution too. Thanks.

[@m.kpatel161]

Excellent

[@offrampc]

2^x = a. Keep squaring and moving the 2's to the right side until you get a^15 = 2^75. a = 2^5. x = 5.

[@ShriH-d1o]

Raise both sides by 16; =>get 2^{(8x+8)+(4x-4)+(2x+2)+(x-1)}=32^16; => 2^(15x+5)=2^(80) =>15x+5=80; => x= 5

[@فیروزاهنگری]

[(2^x+1)^8(2^x-1)^4(2x+1)^2(2^x-1)]^1/16=32 , 2^15x+5=2^80 15x+5=80 x=5

[@RashmiRay-c1y]

2^(x+1)=a and 2^(x-1)=b. Then 32=[a[b[ab^1/2]^1/2]^1/2]^1/2= [a[a^1/2 b^5/4]^1/2]^1/2= a^5/8 b^5/16 = 2^[15/16 x +5/16]. So, 15/16 x +5/16 = 5 and therefore, x=5.

[@RyanLewis-Johnson-wq6xs]

Sqrt[2^(5+1)Sqrt[2^(5-1)Sqrt[2^(5+1)Sqrt[2^(5-1)]]]]=32 x=5 It’s in my head.

[@jasonvuong2656]

Prove it was in your head. You copied the question and the answer and a sentence “it’s in my head”. LOL Here is what I do to get same answer: square both sides, Divide 2^(5+1) both sides Square both sides Divide 2^(5-1) both sides Square both sides Divide 2^(5+1) both sides Square both sides Divide 2^(5-1) both side Then I get 1 = 2^(75-15x) 1=2^0 So, 75-15x = 0 75=15x Then X = 5.

[@ManojkantSamal]

(8x+8+4x-4+2x+2+x-1)/16 =(15x+5)/16 So, 2^{(15x+5)/16}=2^5 So, (15x+5)/16 =5 15x+5=80 15x=80-5=75 X=75/15=5

[@key_board_x]

√[2^(x + 1) * √{2^(x - 1) * √[2^(x + 1) * √2^(x - 1)]}] = 32 Let: a = 2^(x + 1) Let: b = 2^(x - 1) √[a.√{b.√[a.√b]}] = 32 Let's calculate: a/b a/b = 2^(x + 1) / 2^(x - 1) a/b = 2^[(x + 1) - (x - 1)] a/b = 2^(x + 1 - x + 1) a/b = 2^(2) a = 4b Restart from the equation √[a.√{b.√[a.√b]}] = 32 → where: a = 4b √[4b.√{b.√[4b.√b]}] = 2⁵ → by squaring both sides 4b.√{b.√[4b.√b]} = 2¹º → by dividing by (2²) both sides b.√{b.√[4b.√b]} = 2⁸ √{b.√[4b.√b]} = 2⁸/b → by squaring both sides b.√[4b.√b] = 2¹⁶/b² √[4b.√b] = 2¹⁶/b³ → by squaring both sides 4b.√b = 2³²/b⁶ → by dividing by (2²) both sides b.√b = 2³º/b⁶ √b = 2³º/b⁷ → by squaring both sides b = 2⁶º/b¹⁴ b¹⁵ = 2⁶º b = 2⁴ → recall: b = 2^(x - 1) 2^(x - 1) = 2⁴ x - 1 = 4 x = 5

[@Fjfurufjdfjd]

χ=5

[@Quest3669]

3x+1= 16 or X= 5

[@mmk9456aust]

let a= 2^(x+1)√2^(x-1) √(a√a)=2^5 a¾= 2^5 a= 2^(20/3) 2^(x+1)√2^(x-1) = 2^(20/3) 2^(x+1+x/2-1/2) = 2^(20/3) 2^(3x+1) = 2^(40/3) 3x+1 =40/3 x= 37/9 = 4 + 1/9 not sure why i dont get same answer with my method tho😂

[@潘博宇-k4l]

X=5.