问题
解答题
(1)设lg2=a,lg3=b,用a,b表示log512 (2)已知x
|
答案
(1)∵lg2=a,lg3=b,
∴log512=lg12 lg5
=lg3+2lg2 lg10-lg2
=
.b+2a 1-a
(2)∵x
+x-1 2
=3,1 2
∴x2+x-2-2 x
+x-3 2
-33 2
=(x+x-1)2-4 (x
+x-1 2
)(x-1 +x- 1) -31 2
=
,[(x
+x-1 2
)2-2]2-41 2 (x
+x-1 2
)[(x1 2
+x-1 2
)2-3]-31 2
∵x
+x-1 2
=3,1 2
∴原式=
=3.(32-2)2-4 3(32-3)-3