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

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

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.

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

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.