新高考數(shù)學(xué)一輪復(fù)習(xí)精講精練8.7 指數(shù)運(yùn)算及指數(shù)函數(shù)（基礎(chǔ)版）（原卷版）

8.7指數(shù)運(yùn)算及指數(shù)函數(shù)（精講）（基礎(chǔ)版）思維導(dǎo)圖思維導(dǎo)圖考點(diǎn)呈現(xiàn)考點(diǎn)呈現(xiàn)例題剖析例題剖析考點(diǎn)一指數(shù)的運(yùn)算【例1】（2022·全國(guó)·高三專題練習(xí)）化簡(jiǎn)：（1）SKIPIF1<0（2）SKIPIF1<0(a>0，b>0).（3）SKIPIF1<0.【一隅三反】1．（2023·全國(guó)·高三專題練習(xí)）計(jì)算：(1)SKIPIF1<0(2)SKIPIF1<0；(3)SKIPIF1<0(4)求值：SKIPIF1<02．（2023·全國(guó)·高三專題練習(xí)）已知SKIPIF1<0，且SKIPIF1<0，求下列各式的值：(1)SKIPIF1<0；(2)SKIPIF1<0；(3)SKIPIF1<0．3（2023·全國(guó)·高三專題練習(xí)）（1）計(jì)算：SKIPIF1<0；（2）已知SKIPIF1<0是方程SKIPIF1<0的兩根，求SKIPIF1<0的值.考點(diǎn)二指數(shù)函數(shù)的三要素【例2-1】（2022大同期中）函數(shù)SKIPIF1<0是指數(shù)函數(shù)，則有（）A．a(chǎn)＝1或a＝3 B．a(chǎn)＝1 C．a(chǎn)＝3 D．a(chǎn)＞0且a≠1【例2-2】（2022贛州）函數(shù)SKIPIF1<0的值域?yàn)椋ǎ〢．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0【一隅三反】1．（2022保山月考）若函數(shù)SKIPIF1<0是指數(shù)函數(shù)，則（）A．SKIPIF1<0或SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0且SKIPIF1<02．（2022湖北期末）已知實(shí)數(shù)a的取值能使函數(shù)SKIPIF1<0的值域?yàn)镾KIPIF1<0，實(shí)數(shù)b的取值能使函數(shù)SKIPIF1<0的值域?yàn)镾KIPIF1<0，則SKIPIF1<0（）A．4 B．5 C．6 D．73．（2022·全國(guó)·高三專題練習(xí)）已知函數(shù)SKIPIF1<0的定義域?yàn)镾KIPIF1<0，則SKIPIF1<0_________．4．（2022·上?！じ呷_(kāi)學(xué)考試）若函數(shù)SKIPIF1<0的值域?yàn)镾KIPIF1<0，則實(shí)數(shù)SKIPIF1<0的取值范圍為_(kāi)_____．考點(diǎn)三指數(shù)函數(shù)的性質(zhì)【例3-1】（2023·全國(guó)·高三專題練習(xí)）已知函數(shù)SKIPIF1<0（SKIPIF1<0為常數(shù)）．若SKIPIF1<0在區(qū)間SKIPIF1<0上是增函數(shù)，則a的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0【例3-2】（2022·陜西·武功縣普集高級(jí)中學(xué)高三階段練習(xí)（文））設(shè)函數(shù)SKIPIF1<0則滿足SKIPIF1<0的實(shí)數(shù)SKIPIF1<0的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0【例3-3】（2022·黑龍江·雙鴨山一中高三開(kāi)學(xué)考試）已知SKIPIF1<0，則a，b，c大小關(guān)系為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0【一隅三反】1．（2023·全國(guó)·高三專題練習(xí)）已知SKIPIF1<0，則SKIPIF1<0的大小關(guān)系為（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<02．（2023·全國(guó)·高三專題練習(xí)）若關(guān)于SKIPIF1<0的不等式SKIPIF1<0（SKIPIF1<0）恒成立，則實(shí)數(shù)SKIPIF1<0的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．（2022·上海長(zhǎng)寧·二模）若函數(shù)SKIPIF1<0存在反函數(shù)，則常數(shù)SKIPIF1<0的取值范圍為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．（2023·全國(guó)·高三專題練習(xí)）若函數(shù)SKIPIF1<0在SKIPIF1<0上單調(diào)遞減，則k的取值范圍為_(kāi)___________．4．（2023·全國(guó)·高三專題練習(xí)）已知定義域?yàn)镽的函數(shù)SKIPIF1<0則關(guān)于t的不等式SKIPIF1<0的解集為_(kāi)_______.考點(diǎn)四指數(shù)函數(shù)的綜合運(yùn)用【例4】（2022南京月考）已知函數(shù)SKIPIF1<0函數(shù)SKIPIF1<0（1）若SKIPIF1<0的定義域?yàn)镽求實(shí)數(shù)m的范圍.（2）若函數(shù)y=|f(x)-3|-k=0在區(qū)間[-2，1]上有且僅有1個(gè)解，求實(shí)數(shù)k的范圍，（3）是否存在實(shí)數(shù)a，b使得函數(shù)SKIPIF1<0的定義域?yàn)閇a，b]且值域?yàn)閇2a，2b]？若存在，求出a，b的值；若不存在，請(qǐng)說(shuō)明理由.【一隅三反】1．（2023·全國(guó)·高三專題練習(xí)）（多選）已知函數(shù)SKIPIF1<0，則（

）A．SKIPIF1<0為偶函數(shù) B．SKIPIF1<0是增函數(shù)C．SKIPIF1<0不是周期函數(shù) D．SKIPIF1<0的最小值為SKIPIF1<02．（2022·全國(guó)·高三專題練習(xí)）（多選）已知函數(shù)SKIPIF1<0，則下列結(jié)論正確的有（

）A．SKIPIF1<0的圖象關(guān)于坐標(biāo)原點(diǎn)對(duì)稱 B．SKIPIF1<0的圖象關(guān)于SKIPIF1<0軸對(duì)稱C．SKIPIF1<0的最大值為1 D．SKIPIF1<0在定義域上單調(diào)遞減3．（2022張掖期末）已知函數(shù)SKIPIF1<0（SKIPIF1<0）在區(qū)間SKIPIF1<0上有最大值SKIPIF1<0和最小值SKIPIF1<0.設(shè)SKIPIF1<0.（1）求SKIPIF1<0，SKIPIF1<0的值；（2）若不等式SKIPIF1<0在SKIPIF1<0上有解，求實(shí)數(shù)SKIPIF1<0的取值范圍.8.7指數(shù)運(yùn)算及指數(shù)函數(shù)（精練）（基礎(chǔ)版）題組一題組一指數(shù)的運(yùn)算（2022·全國(guó)·高三專題練習(xí)）（1）計(jì)算SKIPIF1<0；（2）若SKIPIF1<0，求SKIPIF1<0的值．2．（2022·全國(guó)·高三專題練習(xí)）化簡(jiǎn)下列各式：（1）SKIPIF1<0－SKIPIF1<0－π0；（2）SKIPIF1<03．（2022·全國(guó)·高三專題練習(xí)）化簡(jiǎn)下列各式(其中各字母均為正數(shù))．（1）SKIPIF1<0；（2）SKIPIF1<0；（3）SKIPIF1<0；（4）SKIPIF1<0.4（2022·全國(guó)·高三專題練習(xí)）（1）計(jì)算：SKIPIF1<0；（2）化簡(jiǎn)：SKIPIF1<0.5．（2022·全國(guó)·高三專題練習(xí)）分別計(jì)算下列數(shù)值：（1）SKIPIF1<0；（2）已知SKIPIF1<0，SKIPIF1<0，求SKIPIF1<0.題組二題組二指數(shù)函數(shù)的三要素1．（2022張家口）函數(shù)SKIPIF1<0的值域?yàn)椋ǎ〢．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．（2022湖南）若不等式SKIPIF1<0恒成立，則實(shí)數(shù)SKIPIF1<0的取值范圍是（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．（2022嫩江月考）（多選）函數(shù)y＝(a2－4a＋4)ax是指數(shù)函數(shù)，則a的值不可以是（）A．4 B．3 C．2 D．14．（2022長(zhǎng)春月考）已知函數(shù)f(x)=x2?2，x<?12x?1，x≥?1，則函數(shù)A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<05．（2021·全國(guó)乙卷）下列函數(shù)中最小值為4的是（）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<06．（2022·北京市第二十二中學(xué)高三開(kāi)學(xué)考試）下列函數(shù)中，定義域與值域均為R的是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<07．（2022·江蘇·礦大附中高三階段練習(xí)）（多選）函數(shù)SKIPIF1<0的定義域?yàn)镾KIPIF1<0，值域?yàn)镾KIPIF1<0，下列結(jié)論中一定成立的結(jié)論的序號(hào)是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<06．（2022奉賢期中）指數(shù)函數(shù)SKIPIF1<0的圖像經(jīng)過(guò)點(diǎn)SKIPIF1<0，則該指數(shù)函數(shù)的表達(dá)式為．7．（2022定遠(yuǎn)月考）已知SKIPIF1<0，且SKIPIF1<0，若函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上的最大值為10，則SKIPIF1<0.題組三題組三指數(shù)函數(shù)的性質(zhì)1．（2022·重慶南開(kāi)中學(xué)高三階段練習(xí)）若命題“SKIPIF1<0”為真命題，則實(shí)數(shù)SKIPIF1<0的取值范圍為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．（2022·黑龍江·牡丹江市第三高級(jí)中學(xué)高三階段練習(xí)）已知SKIPIF1<0，則SKIPIF1<0的大小關(guān)系為（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<03．（2023·全國(guó)·高三專題練習(xí)）已知SKIPIF1<0，SKIPIF1<0，則a、b、c的大小關(guān)系為（）A．a(chǎn)＜b＜c B．c＜a＜b C．b＜a＜c D．c＜b＜a4．（2023·全國(guó)·高三專題練習(xí)）三個(gè)數(shù)a＝0.42，b＝log20.3，c＝20.6之間的大小關(guān)系是（

）A．a(chǎn)＜c＜b B．a(chǎn)＜b＜c C．b＜a＜c D．b＜c＜a5．（2022·山東·棗莊市第三中學(xué)高三開(kāi)學(xué)考試）已知函數(shù)SKIPIF1<0，若存在非零實(shí)數(shù)SKIPIF1<0，使得SKIPIF1<0成立，則實(shí)數(shù)SKIPIF1<0的取值范圍是___________.6．（2022·全國(guó)·高三專題練習(xí)）已知函數(shù)SKIPIF1<0，若方程SKIPIF1<0有解，則實(shí)數(shù)SKIPIF1<0的取值范圍是_________．7．（2022·全國(guó)·高三專題練習(xí)）已知函數(shù)SKIPIF1<0，若SKIPIF1<0，使得SKIPIF1<0，則實(shí)數(shù)a的取值范圍是___________.8．（2022遂寧期末）已知方程SKIPIF1<0有兩個(gè)不相等實(shí)根，則SKIPIF1<0的取值范圍為．9（2022河北）．設(shè)函數(shù)f（x）=x（ex+ae﹣x），x∈R，是偶函數(shù)，則實(shí)數(shù)a=．10．（2022云南）要使函數(shù)y=1+2x+a?4x在（x∈（﹣∞，1]）有y＞0恒成立，則實(shí)數(shù)a的取值范圍是．題組四題組四指數(shù)函數(shù)的綜合運(yùn)用1．（2022泗縣開(kāi)學(xué)考）已知函數(shù)SKIPIF1<0的定義域?yàn)镾KIPIF1<0.（1）求SKIPIF1<0；（2）當(dāng)SKIPIF1<0時(shí)，求SKIPIF1<0的最小值.2（2022石家莊期末）設(shè)指數(shù)函數(shù)SKIPIF1<0，冪函數(shù)SKIPIF1<0.（