若log7 (2√2+1)+log2 (√2-1）=a,把log7 (2√2-1）+log2 (√2+1）表示为a的代数式_数学解答

若log7 (2√2+1)+log2 (√2-1）=a,把log7 (2√2-1）+log2 (√2+1）表示为a的代数式

人气：459 ℃　时间：2020-06-21 15:26:11

解答

两式相加
log7 (2√2+1)+log2 (√2-1）+log7 (2√2-1）+log2 (√2+1）
=log7 [(2√2+1)(2√2-1）] +log2 [(√2-1)(√2+1）]
=log7 7 + log2 1
=1+0=1
又log7 (2√2+1)+log2 (√2-1）=a
所以
log7 (2√2-1）+log2 (√2+1）=1-a