помогите решить систему x^y=y^x ; x^5=y^3. решите в положительных числах систему уравнений

Ответ
{ x^y=y^x
{ x^5=y^3

{ log(x) y^x = y
{ log(x) y^3 = 5

{ x*log(x) y = y
{ 3*log(x) y = 5

{ log(x) y = y/x
{ log(x) y = 5/3
=>
y/x = 5/3
y = (5/3)*x
=>
x^5 = y^3 =>
x^5 = (5x/3)^3
x^5 = (5/3)^3 * x^3
x^5/x^3 = (5/3)^3
x^2 = (5/3)^3
x = V(5/3)^3 = (5/3)^(3/2)
y = (5/3)*x = (5/3) * (5/3)^(3/2) = (5/3)^(5/2)
=>
Проверка
x^5 = y^3
[(5/3)^(3/2)]^5 = [(5/3)^(5/2)]^3
(5/3)^(3/2*5) = (5/3)^(5/2*3)
(5/3)^(15/2) = (5/3)^(15/2)
5/3 = 5/3