Question

計(jì)算2log

2

3+log(2+

3

)(

3

-2)2-102+lg2．

Answer 1

分析：先利用對(duì)數(shù)的運(yùn)算法則把2log

2

3+log(2+

3

)(

3

-2)2-102+lg2等價(jià)轉(zhuǎn)化為2log29+log(2+

3

)(2+

3

)-2-10²×10^lg2，進(jìn)一步簡(jiǎn)化為9-2-100×2，由此能求出結(jié)果．

解答：解：2log

2

3+log(2+

3

)(

3

-2)2-102+lg2
=2log29+log(2+

3

)(2+

3

)-2-10²×10^lg2
=9-2-100×2
=193．

點(diǎn)評(píng)：本題考查對(duì)數(shù)的運(yùn)算性質(zhì)的應(yīng)用，是基礎(chǔ)題．解題時(shí)要認(rèn)真審題，仔細(xì)解答，注意合理地進(jìn)行等價(jià)轉(zhuǎn)化．