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Question

If log2(x+y)=log3(xy)=log 25log 0.2, find the values of x and y.

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Solution

Given log2(x+y)=log3(xy)=log 25log 0.2

log2(x+y)=log3(xy)=log 52log 51

log2(x+y)=log3(xy)=2×log 51×log 5

log2(x+y)=log3(xy)=2

log2(x+y)=2 and log3(xy)=2

x+y=22 -----------(1) and xy=32​​​​​​​ ----------(2)

Solving (1) and (2) we get

x=1372 and y=572


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