{\log(97-56\sqrt3)}/{\log\sqrt{7+4\sqrt3} equals which of the following?

Xavier Aptitude Test 2019 Paper

Question : 61 of 98

Marks: +1, -0

{\log(97-56√3)}/{\log√{7+4√3}}

equals which of the following?

Solution:

{\log(97-56√3)}/{\log√{7+4√3}}

={2\log(97-56√3)}/{\log({7+4√3})}

={2\log( 7-4√3)^2}/{\log({7+4√3})}

={4\log( {(7-4√3)(7+4√3)}/(7+4√3)) }/{\log({7+4√3})}

={4\log( {1}/{7+4√3}) }/{\log({7+4√3})}

={-4\log( {7+4√3}) }/{\log({7+4√3})}=-4

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