Question

已知log₇[log₃（log₂x）]=0，那么=    ．

Answer 1

【答案】分析：根據(jù)對(duì)數(shù)的定義先求出log₃（log₂x）=1，再求出log₂x=3，進(jìn)而求出x的值，再代入根據(jù)指數(shù)的運(yùn)算性質(zhì)進(jìn)行化簡(jiǎn)．
解答：解：由log₇[log₃（log₂x）]=0得，log₃（log₂x）=1，則log₂x=3，
解得，x=2³，∴===．
故答案為：．
點(diǎn)評(píng)：本題的考點(diǎn)是對(duì)數(shù)和指數(shù)的運(yùn)算性質(zhì)的應(yīng)用，對(duì)多重對(duì)數(shù)式子化簡(jiǎn)時(shí)，應(yīng)從內(nèi)向外逐層化簡(jiǎn)求值．