Question

if X square + Y square equal to 27 x y then show that log x minus y by 5 equals to half into log x + log y ​

Answer 1

Step-by-step explanation:

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

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

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

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

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

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

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

$\boxed { \pink { log a^{m} = m log a }}$

$\boxed { \orange { log (mn)= log m + log n}}$

$\implies log\left(\frac{x-y}{5} \right)= \frac{1}{2} (log x + log y)$

$Hence , proved$

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