solve for x and y the equation 2lnx −lny =ln(5x−6y)


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Question Number 68899 by Rio Michael last updated on 16/Sep/19

$s o l v e f o r x a n d y t h e e q u a t i o n$ $2 l n x - l n y = l n (5 x - 6 y)$
Commented by kaivan.ahmadi last updated on 16/Sep/19

$i d o n t k n o w . i t h i n k i t i s h a r d .$
Commented by Rio Michael last updated on 16/Sep/19

$t h a n k s s i r$
Commented by kaivan.ahmadi last updated on 16/Sep/19

$l n \frac{x^{2}}{y} = l n (5 x - 6 y) \Rightarrow \frac{x^{2}}{y} = 5 x - 6 y \Rightarrow$ $x^{2} = 5 x y - 6 y^{2} \Rightarrow x^{2} - 5 x y + 6 y^{2} = 0$
Commented by Rio Michael last updated on 16/Sep/19

$x^{2} - 5 x y + 6 y^{2} = 0$ $x (x - 3 y) - 2 y (x - 3 y) = 0$ $(x - 3 y) (x - 2 y) = 0$ $\frac{x}{y} = \frac{3}{1} o r \frac{x}{y} = \frac{2}{1}$ $x = 3, y = 1 o r x = 2, y = 1$
Commented by kaivan.ahmadi last updated on 16/Sep/19

$n i c e$
Commented by Rio Michael last updated on 16/Sep/19

$h o w a b o u t t h e n e x t o n e s i r$
Commented by Rasheed.Sindhi last updated on 17/Sep/19

$Rio Michael sir .$ $x^{2} - 5 x y + 6 y^{2} = 0 : I t h i n k t h a t$ $x & y {c o u l d n}^{'} t b e d e t e r m i n e d u n i q u e l y$ $b y t h i s s i n g l e e q u a t i o n .$ $\frac{x}{y} = \frac{3}{1} ⇏ x = 3, y = 1$ $\frac{x}{y} = \frac{3}{1} \Rightarrow x = 3 k, y = k \forall k \in C$ $x^{2} - 5 x y + 6 y^{2} = 0 \Rightarrow {(3 k)}^{2} - 5 (3 k) (k) + 6 {(k)}^{2} = 0$ $9 k^{2} - 15 k^{2} + 6 k^{2} = 0 \Rightarrow 15 k^{2} - 15 k^{2} = 0 \Rightarrow 0 = 0$
Commented by kaivan.ahmadi last updated on 17/Sep/19

$t h a n k s i r, i t s g e n e r a l$
Commented by Rio Michael last updated on 21/Sep/19

$s o s i r t h e q u e s t i o n i s w r o n g ?$
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