log4(1+√2+√3)+log4(1+√2-√3)的值等于
问题描述：
log4(1+√2+√3)+log4(1+√2-√3)的值等于
答
log4(1+√2+√3)+log4(1+√2-√3)
=log4[(1+√2+√3)(1+√2-√3)]
=log4[(1+√2)^2-(√3)^2]
=log4[3+2√2-3]
=log4(2√2)
=log4(2^3/2)
=ln(2^3/2)/ln4
=3/2*ln2/(2ln2)
=3/4