Question

give reason for the answer ​

Answer 1

option 2 is correct

see the circled pic in attachment...

Answer 2

using property

$log_{a}(b) = \frac{ log_{e}(b) }{ log_{e}(a) }$

therefore,

$log_{a}(x) \times log_{y}(a) = \frac{ ln(x) \times ln(a) }{ ln(a) \times ln(y) } = \frac{ ln(x) }{ ln(y) } = log_{y}(x)$

hence, option (2) is correct