3x^ln5=5y^ln3 and x^ln3=y^ln5

Question

both are simultaneous equation.find the value of x and y.thankyou

Answer 1

3 * x^(ln 5) = 5 * y^(ln 3)

 

x^(ln 3) = y^(ln 5)

 

Raise both sides to the 1/(ln 3) power. You get:

 

x = y^[(ln 5)/(ln 3)]

 

Substitute into the first equation

 

3 * y^[(ln 5)(ln 5)/(ln 3)] = 5 * y^(ln 3)

 

Divide both sides by 3 and y^(ln 3). You get:

 

y^[(ln 5)(ln 5)/(ln 3) - ln 3] = 5/3

 

y^1.26 = 5/3

 

y = 1.5003 which is approximately 1.5