If log (a+b) +log (b/a) =log(a+b) then
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log a/b + log b/a = log ( a + b)
log ( a/b * b/a ) = log ( a + b )
log 1 = log ( a + b)
So, a + b = 1 .
a = 1 - b
b = 1 - a.
Therefore, If log a/b + log b/a = log (a + b), then a+ b = 1
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