题目

2^log4(2-根号3)^2+3^log(2+根号3)^2
[(1-log6(3)^2+log6(2)*log6(18)]/log6(4)
[(1-log6(3))^2+log6(2)*log6(18)]/log6(4)

提问时间：2020-12-27

答案

2^log4(2-√3)^2+3^log9(2+√3)^2
=[4^(1/2)]^log4(2-√3)^2+[9^(1/2)]^log9(2+√3)^2
=4^[(1/2)log4(2-√3)^2]+9^[(1/2)*log9(2+√3)^2]
=4^log4(2-√3)^[2*(1/2)]+9^log9(2+√3)^[2*(1/2)]
=4^log4(2-√3)+9^log9(2+√3)
=(2-√3)+(2+√3)
=4
{[1-log6(3)]^2+log6(2)*log6(18)}/log6(4)
={[log6(6)-log6(3)]^2+log6(2)*log6(18)}/log6(4)
={[log6(6/3)]^2+log6(2)*log6(18)}/log6(4)
={[log6(2)]^2+log6(2)*log6(18)}/log6(4)
={log6(2)*[log6(2)+log6(18)]}/log6(4)
=[log6(2)*log6(2*18)]/log6(4)
=[log6(2)*log6(36)]/log6(4)
=[log6(2)*log6(6^2)]/log6(4)
=[log6(2)*2*log6(6)]/log6(4)
=2log6(2)/log6(4)
=log6(2^2)/log6(4)
=log6(4)/log6(4)
=1