Question

$1 \div log_{x}(xy)+1 \div log_{y}(xy ) =$
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Answer 1

Answer:

$1 \div log_{x}(xy)+1 \div log_{y}(xy ) \\ \\ = \frac{1}{log_{x}(xy)} + \frac{1}{log_{y}(xy )} \\ \\= \frac{1}{ \frac{log(xy)}{lox} } + \frac{1}{ \frac{log(xy)}{loy} } \\ \\= \frac{logx}{log(xy)} + \frac{logy}{log(xy)} \\ \\= \frac{logx + logy}{log(xy)} \\ \\= \frac{log(xy)}{log(xy)} \\ \\ = 1 \\\\ thus\\ \\ 1 \div log_{x}(xy)+1 \div log_{y}(xy ) = 1$