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solve-for-x-amp-y-x-logy-4-xy-40-




Question Number 55969 by Muhammad bello last updated on 07/Mar/19
   solve   for   x   &  y            x^(logy)    =  4          xy    =    40
solveforx&yxlogy=4xy=40
Answered by MJS last updated on 07/Mar/19
x^(ln y) =4  ln x ln y =ln 4  (1)  xy=40  ln x +ln y =ln 40  (2)  (1) pq=a ⇒ q=(a/p)  (2) p+q=b ⇒ p+(a/p)=b ⇒ p^2 −bp+a=0 ⇒  ⇒ p=(b/2)±((√(b^2 −4a))/2)  ⇒ q=(b/2)∓((√(b^2 −4a))/2)  ln x =((ln 40)/2)±((√((ln 40)^2 −4ln 4))/2)  ln y =((ln 40)/2)∓((√((ln 40)^2 −4ln 4))/2)  ⇒ (x≈1.52913 ∧ y≈26.1587) ∨ (x≈26.1587 ∧ y≈1.52913)
xlny=4lnxlny=ln4(1)xy=40lnx+lny=ln40(2)(1)pq=aq=ap(2)p+q=bp+ap=bp2bp+a=0p=b2±b24a2q=b2b24a2lnx=ln402±(ln40)24ln42lny=ln402(ln40)24ln42(x1.52913y26.1587)(x26.1587y1.52913)

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