Question

計(jì)算：lne3+(lg5)2+lg2×lg50-(

1

27

)-

1

3

．

Answer 1

分析：我們分別利用對(duì)數(shù)的運(yùn)算性質(zhì)及指數(shù)的運(yùn)算性質(zhì)對(duì)式子進(jìn)行化簡(jiǎn)，結(jié)合完成公式即可求出答案．

解答：解：lne3+(lg5)2+lg2×lg50-(

1

27

)-

1

3

=3+（lg5）²+lg2×lg（2×5²）-3
=（lg5）²+lg2×（lg2+2lg5）
=（lg5）²+2（lg2×lg5）+（lg2）²
=（lg2+lg5）²
=1

點(diǎn)評(píng)：本題考查的知識(shí)點(diǎn)是對(duì)數(shù)的運(yùn)算性質(zhì)及指數(shù)的運(yùn)算性質(zhì)，是對(duì)對(duì)數(shù)的運(yùn)算性質(zhì)及指數(shù)的運(yùn)算性質(zhì)應(yīng)用的直接考查，熟練掌握對(duì)數(shù)的運(yùn)算性質(zhì)及指數(shù)的運(yùn)算性質(zhì)是解答本題的關(guān)鍵．