新高考數(shù)學(xué)一輪復(fù)習(xí)提升訓(xùn)練3.4 對數(shù)運算及對數(shù)函數(shù)（精講）（原卷版）

3.4對數(shù)運算及對數(shù)函數(shù)（精講）（提升版）思維導(dǎo)圖思維導(dǎo)圖考點呈現(xiàn)考點呈現(xiàn)例題剖析例題剖析考點一對數(shù)運算【例1】（2022·全國·高三專題練習(xí)）化簡求值（1）SKIPIF1<0；（2）SKIPIF1<0；.（3）SKIPIF1<0；．（4）SKIPIF1<0.【一隅三反】（2022·全國·高三專題練習(xí)）化簡求值：（1）SKIPIF1<0．（2）SKIPIF1<0；（3）SKIPIF1<0.（4）SKIPIF1<0（5）SKIPIF1<0．考點二對數(shù)函數(shù)的單調(diào)性【例2-1】（2022·全國·高三專題練習(xí)）若函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0內(nèi)單調(diào)遞增，則實數(shù)SKIPIF1<0的取值范圍為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0【例2-2】（2022·天津·南開中學(xué)二模）已知函數(shù)SKIPIF1<0是R上的單調(diào)函數(shù)，則實數(shù)a的取值范圍為（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0【一隅三反】1．（2022·全國·高三專題練習(xí)）函數(shù)SKIPIF1<0的單調(diào)遞增區(qū)間為____________．2．（2022·全國·高三專題練習(xí)）已知函數(shù)f(x)＝lg(x2－2x－3)在(－∞，a)單調(diào)遞減，則a的取值范圍是（

）A．(－∞，－1] B．(－∞，2] C．[5，＋∞) D．[3，＋∞)3．（2021·天津市武清區(qū)大良中學(xué)高三階段練習(xí)）若函數(shù)SKIPIF1<0在R上單調(diào)遞增，則實數(shù)a的取值范圍是_______4．（2022·河北）已知函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上是增函數(shù)，求實數(shù)SKIPIF1<0的取值范圍_____．考點三對數(shù)函數(shù)的值域（最值）【例3-1】（2022·全國·高三專題練習(xí)）函數(shù)SKIPIF1<0的最小值為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．0【例3-2】（2022·四川·宜賓市教科所三模）若函數(shù)SKIPIF1<0的值域為SKIPIF1<0，則SKIPIF1<0的取值范圍是(

)A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0【例3-3】（2022·重慶·模擬預(yù)測）若函數(shù)SKIPIF1<0有最小值，則實數(shù)a的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0【一隅三反】1．（2022·全國·高三專題練習(xí)）已知SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0的值域為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．（2022·全國·高三專題練習(xí)）若函數(shù)SKIPIF1<0且SKIPIF1<0的值域為SKIPIF1<0，則SKIPIF1<0的取值范圍為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．（2022·全國·高三專題練習(xí)）若函數(shù)SKIPIF1<0的值域為SKIPIF1<0，則實數(shù)SKIPIF1<0的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．（2022·全國·高三專題練習(xí)）已知函數(shù)SKIPIF1<0的值域為R，則實數(shù)a的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0考點四對數(shù)式比較大小【例4-1】（2022·江蘇常州·模擬預(yù)測）已知SKIPIF1<0，則正確的大小順序是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0【例4-2】（2022·新疆烏魯木齊·模擬預(yù)測（理））設(shè)SKIPIF1<0，則（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0【一隅三反】1．（2022·浙江·模擬預(yù)測）己知實數(shù)SKIPIF1<0，且SKIPIF1<0，則（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．（2022·全國·模擬預(yù)測）定義在R上的函數(shù)SKIPIF1<0滿足SKIPIF1<0，當(dāng)SKIPIF1<0時，SKIPIF1<0，設(shè)SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，則a，b，c的大小關(guān)系是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．（2022·浙江金華·三模）若函數(shù)SKIPIF1<0，設(shè)SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，則下列選項正確的是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<04．（2022·廣東佛山·三模）（多選）已知SKIPIF1<0，則下列不等式成立的是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0考點五解對數(shù)式不等式【例5-1】（2022·河南濮陽）已知函數(shù)SKIPIF1<0是R上的偶函數(shù)，且SKIPIF1<0在SKIPIF1<0上恒有SKIPIF1<0，則不等式SKIPIF1<0的解集為（

）A．SKIPIF1<0 B．1,e2 C．SKIPIF1<0 D．SKIPIF1<0【例5-2】（2022·湖北·二模）已知函數(shù)SKIPIF1<0，則使不等式SKIPIF1<0成立的x的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0【一隅三反】1．（2021·河南·高三階段練習(xí)（理））設(shè)函數(shù)SKIPIF1<0，則不等式SKIPIF1<0的解集為（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<02．（2021·江西·奉新縣第一中學(xué)高三階段練習(xí)（理））已知函數(shù)SKIPIF1<0，若SKIPIF1<0，則實數(shù)a的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．（2021·安徽·高三階段練習(xí)（理））已知函數(shù)SKIPIF1<0，則不等式SKIPIF1<0的解集為（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0考點六對數(shù)函數(shù)的定點【例6】（2021·四川·德陽五中）若函數(shù)SKIPIF1<0的圖象經(jīng)過定點SKIPIF1<0，且點SKIPIF1<0在角SKIPIF1<0的終邊上，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0【一隅三反】1．（2022·全國·高三專題練習(xí)）已知函數(shù)SKIPIF1<0（SKIPIF1<0且SKIPIF1<0）的圖象過定點SKIPIF1<0，且角SKIPIF1<0的終邊經(jīng)過SKIPIF1<0，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．（2022·全國·高三專題練習(xí)）已知正數(shù)SKIPIF1<0，SKIPIF1<0，函數(shù)SKIPIF1<0（SKIPIF1<0且SKIPIF1<0）的圖象過定點SKIPIF1<0，且點SKIPIF1<0在直線SKIPIF1<0上，則SKIPIF1<0的最小值為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．