Question

Please solve this question ​

Answer 1

$heya \\ \\ \\ log_{2}(x + y) = 2 log_{5 {}^{ - 1} }(5) \\ \\ \\ log_{2}(x + y) = - 2 \\ \\ \\ (x + y) = 2 {}^{ - 2} \\ \\ \\ x + y = 1 \div 4.......equation \: \: \: i \\ \\ \\ \\ and \: \: \: \\ \\ \\ log_{3}(x - y) = 2log_{5 {}^{ - 1} }(5) \\ \\ \\ log_{3}(x - y) = - 2 \\ \\ \\ (x - y) = 3 {}^{ - 2} \\ \\ \\ (x - y) = 1 \div 9......equation \: \: \: ii \\ \\ \\ now \: solve \: both \: the \: equations \: we \: get \: \: \: \\ \\ \: x \: = 13 \div 72 \\ \\ \\ and \\ \\ \\ \\ y = 5 \div 72 \\ \\ \\ \\ \\ \\ - - - - - - - - - - - - - - - - \\ \\ \\ formula \: used \\ \\ \\ \\ 1) \: \: \: log(x {}^{n} ) = n log(x) \\ \\ \\ 2) \: \: \: log_{y {}^{a} }(x) = (1 \div a) log_{y}(x)$