Statement - 1 : If `x gt 1` then `log_(10)x lt log_(3)x lt log_(e )x lt log_(2)x`.
Statement - 2 : If `0 lt x lt 1`, then `log_(x)a gt log_(x)b implies a lt b`.

Options

A. Statement - 1 is True, Statement - 2 si True , Statement -2 is a correct explanation for Statement - 1
B. Statement -1 is True, Statement -2 si True, Statemetn -2 is NOT a correct explanation for Statement -1
C. Statement - 1 is True, Statement - 2 is False
D. Statement - 1 is False, Statement - 2 is True

Answer

B

Explanation

Statement -1 : If `x gt 1` then …………..
Since `10gt 3gt egt2`
If `x gt 1, then log, 10 gt log_(x)3 gt log_(x)e gt log_(x)2`
`implies (1)/(log_(10)) gt (1)/(log_(3)x)gt (1)/(log_(e )x)gt (1)/(log_(2)x)`
`implies log_(10)x lt log_(3)x lt log_(e )x lt log_(2)x`