已知log7(2√2+1)+log2（√2-1）=a，则log7（2√2-1）+log2（√2+1）=_______.

利用分子有理化，分子分母同乘以分子的有理化因子，向已知条件转化。
log7（2√2-1）+log2（√2+1）
=log7 [(8-1)/(2√2+1)] + log2 [(2-1)/(√2-1)]
=1- log7 (2√2+1) - log2 (√2-1)
=1- [log7(2√2+1)+log2（√2-1）]
=1-a.

log7（2√2-1）+log2（√2+1）
=log7[7/(2√2+1)）+log2[1/(√2-1)]
=1-log7(2√2+1)-log2(√2-1)
=1-a.

设log7（2√2-1）+log2（√2+1）=X 则a+X=log7(2√2+1)（2√2-1）+log2（√2-1）（√2+1）=1+0=1 则X=1-a log7（2√2-1）+log2（√2+1）=1-a

1-a