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

问题描述:

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.