Log-y-x-Log-x-y-64-find-x-and-y-

Question Number 82821 by VBash last updated on 24/Feb/20

{L o g}_{y} x + {L o g}_{x} y = 64

f i n d x a n d y

Commented by MJS last updated on 24/Feb/20

one equation in two unknown gives a

parametric solution

\frac{\ln x}{\ln y} + \frac{\ln y}{\ln x} = 64; x > 0 \land y > 0

\Rightarrow

{(\ln x)}^{2} - (64 \ln y) \ln x + {(\ln y)}^{2} = 0

\Rightarrow

\ln x = (32 \pm \sqrt{1023}) \ln y

\Rightarrow

x = y^{32 \pm \sqrt{1023}} \forall y > 0

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