(log5根号2乘以log79)除(log53分之1乘log73倍的根号4)+log2(根号(3+根号5)—根(3-根号5))

Question

(log5根号2乘以log7 9)除(log5 3分之1乘log7 3倍的根号4)+log2(根号(3+根号5)—根(3-根号5))

Answer 1

log7 3倍的根号4,这个应该是4的开立方
原式=log(5,2)log(7,3)/[-log(5,3)log(7,4)/3]+log(2,[根号(3+根号5)—根(3-根号5)])
=-3log(3,2)log(4,3)+log(2,[根号(3+根号5)—根(3-根号5)]^2)/2
=-3log(3,2)/log(3,4)+log(2,{(3+根号5)+(3-根号5)-2根号[(3+根号5)(3-根号5)]})/2
=-3log(4,2)+log(2,2)/2
=-3/2+1/2
=-1