Question

計(jì)算：(-

27

8

)-

2

3

+(2-

3

)0-

1

9

×log29•log34=

1

．

Answer 1

分析：化負(fù)指數(shù)為正指數(shù)，化分?jǐn)?shù)指數(shù)冪為根式，利用對(duì)數(shù)的換底公式化簡(jiǎn)后進(jìn)行計(jì)算．

解答：解：(-

27

8

)-

2

3

+(2-

3

)0-

1

9

×log29•log34
=

1

3 [-( 3 2 )3]2

+1-

1

9

×

lg9

lg2

×

lg4

lg3

=

1

( 3 2 )2

+1-

1

9

×

2lg3

lg2

×

2lg2

lg3

=

4

9

+1-

4

9

=1．
故答案為：1．

點(diǎn)評(píng)：本題考查了有理指數(shù)冪的化簡(jiǎn)與求值，考查了對(duì)數(shù)的換底公式及運(yùn)算性質(zhì)，關(guān)鍵是第一項(xiàng)的化簡(jiǎn)，是基礎(chǔ)的計(jì)算題．