Question

In the formula logaxy = logax + logay,
which of the following is true?
1) x>0, y>0, a=1
2) x<0 y<O, a=1
3)a>0, y>0, x=1
4) x>0, y>0,a not equal to 1
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Answer 1

Answer:

logaxy = m (let)

xy = a^m

if a= 1, then xy has to be 1

similarly x has to be 1 and y has to be 1

now, log11 has infinite solution since, 1 raised to any power is 1. hence, the formula will have no meaning.

so, for meaningful formula, a needs to be not equal to 1. hence option d