Question

if x^2+y^2=10xy,then prove that 2log (x-y) =log x + log y + 3log 2​

Answer 1

Step-by-step explanation:

${x}^{2} + {y}^{2} = 10xy \\ \\ \\ {(x - y)}^{2} = {x}^{2} + {y}^{2} - 2xy \\ \\ \\ {(x - y)}^{2} = 10xy - 2xy \\ \\ \\ {(x - y)}^{2} = 8xy \\ \\ \\ taking \: log \: on \: both \: sides \: \\ \\ \\ 2 log(x - y) = log(8xy) \\ \\ \\ = log(x) + log(y) + 3 log(2)$

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