Question

If log (x-y/5)=1/2 logx+1/2 logy,
show that x 2 +y2 =27xy.

Answer 1

it should be your answer.

Answer 2

$Given \:log \Big(\frac{(x-y)}{5}\Big) = \frac{1}{2} log x + \frac{1}{2} log y$

/* Multiplying each term by 2 , we get */

$\implies \:2log \Big(\frac{(x-y)}{5}\Big) = log x + log y$

$\implies \:log \Big(\frac{(x-y)}{5}\Big)^{2} = log (xy)$

$\boxed { \pink { log x + log y = log (xy) }}$

$\implies \Big(\frac{(x-y)}{5}\Big)^{2} = (xy)$

$\implies \frac{(x-y)^{2}}{5^{2}} = xy$

$\implies \frac{(x-y)^{2}}{25} = xy$

$\implies (x-y)^{2}= 25xy$

$\implies x^{2} + y^{2} - 2xy = 25xy$

$\implies x^{2} + y^{2} = 25xy + 2xy$

$\implies x^{2} + y^{2} = 27xy$

$Hence \:proved$

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