Answers

2015-06-12T20:27:42+05:30
Given that log2(x+y) = log3(x-y) = log25/log0.2

log25/log0.2 
= log25/log (1/5)
= log25/(- log 5)
= - log5 25
= -2
 

log_2(x+y) = -2\\ \\ \Rightarrow  x+y = 2^{-2}\\ \\ \Rightarrow  x+y = 1/4

log3(x-y) = -2\\\\ \Rightarrow x-y = 3^{-2}\\\\ \Rightarrow x-y = 1/9

Adding\ them,\\ \\2x =  \frac{1}{4} +  \frac{1}{9} \\ \\ \Rightarrow 2x =  \frac{9+4}{36} = \frac{13}{36} \\ \\ \Rightarrow x = \frac{13}{72}

y =  \frac{1}{4} - \frac{13}{72} =  \frac{18-13}{72}  =  \frac{5}{72}


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