Question

Rozwiąż równania

[2^17]*4-[16^4]*3=5*([4^7]*x-3*[2^17])


[27^3]*2x-[3^9]=[3^10]*x+2*[3^9]

legenda
[x^y]- x do potęgi y

Answer 1

[2^17]*4-[16^4]*3=5*([4^7]*x-3*[2^17])
[ 2¹⁷]*2² - [ (2)⁴]⁴*3 = 5*[(2²)⁷*x - 3*(2¹⁷)]
2¹⁹ - 2¹⁶*3 = 5*[ 2¹⁴*x - 3*2¹⁷]
2¹⁹(2³ -3) = 5*2¹⁴*(x - 3*2³)
2¹⁹*(8-3) = 5*2¹⁴(x -3*2³)
2¹⁶*5 = 5* 2¹⁴( x -24) /:5*2¹⁴
2² = ( x -24)
( x -24) = 2²
x -24 = 4
x = 24 + 4
x = 28



[27^3]*2x - [3^9] = [3^10]*x + 2*[3^9]
[(3³)³]*2x - [3⁹] = [ 3¹°]*x + 2*[3⁹]
3⁹*2x -3⁹ = 3⁹(3x + 2)
3⁹(2x -1) = 3⁹(3x +2) /:3 do potęgi 9
2x - 1 = 3x +2
2x -3x = 2 +1
-x = 3
x = -3