log4^(1+根号2+根号3）+log4^（1+根号2-根号3）

=log4^[两个括号相乘]

真数=[(1+√2)+√3][(1+√2)-√3]
=(1+√2)^2-3
=2√2

所以原式=log4^(2√2)
=lg(2√2)/lg4
=lg2^(3/2)/lg2^2
=(3/2)lg2/2lg2
=3/4

log4(1+根号2+根号3)+log4(1+根号2--根号3）=log4((1+根号2+根号3)(1+根号2-根号3）)=log4((1+根号2)的平方-3)=log4(2根号2)