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Evaluate: lim(x->1)sec(pi/(2x))logxdot...

Evaluate: `lim_(x->1)sec(pi/(2x))logxdot`

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We have, `underset(xto1)lim(log_(e)x)/("cos"(pi)/(2^(x)))=underset(xto1)lim(log(1+(x-1)))/(underset(xto1)lim(sin((pi)/(2)-(pi)/(2^(x))))/(((pi)/(2)-(pi)/(2^(x))))).underset(xto1)lim(x-1)/((pi)/(2)-(pi)/(2^(x)))`
`=underset(xto1)lim(x-1)/(pi((2^(x-1)-1)/(2^(x))))`
`=underset(xto1)lim(2^(x))/(pi).(x-1)/(2^(x-1)-1)`
`=(2)/(pilog2)`
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