Question

有以下四個(gè)結(jié)論①lg（lg10）=0②lg（lne）=0 ③若10=lgx，則x=10 ④若e=lnx，則x=e²，其中正確的是

1. A.
   ①③
2. B.
   ②④
3. C.
   ①②
4. D.
   ③④

Answer 1

C
分析：通過底數(shù)的對(duì)數(shù)是1，1的對(duì)數(shù)為0判斷出①②對(duì)；通過對(duì)數(shù)式與指數(shù)式間的轉(zhuǎn)化判斷出③④錯(cuò)．
解答：對(duì)于①∵lg（lg10）=lg1=lg0，故①對(duì)
對(duì)于②∵lg（lne）=lg1=0∴②對(duì)
對(duì)于③，∵10=lgx∴x=10¹⁰∴③錯(cuò)
對(duì)于④，∵e=lnx∴x=e^e∴④錯(cuò)
故選C
點(diǎn)評(píng)：本題考查兩個(gè)特殊的對(duì)數(shù)值：底數(shù)的對(duì)數(shù)是1，1的對(duì)數(shù)為0、考查對(duì)數(shù)式與指數(shù)式間的互化．