Question

（1）求值：lg52+

2

3

lg8+lg5•lg20+(lg2)2
（2）求值：(0.0081)-

1

4

-[3×(

7

8

)0]-1×[81-0.25+(3

3

8

)-

1

3

]-

1

2

-10×0.027

1

3

．

Answer 1

（1）lg52+

2

3

lg8+lg5•lg20+(lg2)2
=2lg5+

2

3

lg23+lg5(1+lg2)+(lg2)2
=2lg5+2lg2+lg5（1+lg2）+（lg2）²
=2（lg5+lg2）+lg5+lg5•lg2+（lg2）²
=2+lg5+lg2（lg5+lg2）=3．
（2）(0.0081)-

1

4

-[3×(

7

8

)0]-1×[81-0.25+(3

3

8

)-

1

3

]-

1

2

-10×0.027

1

3

=((0.3)4)-

1

4

-3-1×[(34)-

1

4

+(

3

2

)-1]-

1

2

-10×((0.3)3)

1

3

=

10

3

-

1

3

(

1

3

+

2

3

)-

1

2

-10•0.3
=

10

3

-

1

3

-3
=0．