新高考數(shù)學(xué)一輪復(fù)習(xí)精講精練8.8 對數(shù)運(yùn)算及對數(shù)函數(shù)（基礎(chǔ)版）（原卷版）

8.8對數(shù)運(yùn)算及對數(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)一對數(shù)的運(yùn)算【例1】（2022太原）計(jì)算下列各式的值：（1）SKIPIF1<0；（2）SKIPIF1<0.（3）SKIPIF1<0；（4）SKIPIF1<0..【一隅三反】（2022廣東湛江）計(jì)算下列各式：（1）SKIPIF1<0（2）SKIPIF1<0；（3）SKIPIF1<0．（4）SKIPIF1<0.（5）log6(log264)＋SKIPIF1<0.（6）SKIPIF1<0考點(diǎn)二對數(shù)函數(shù)的三要素【例2-1】（2022太原）函數(shù)SKIPIF1<0的定義域是（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0【例2-2】（2022河南）函數(shù)f(x)＝SKIPIF1<0SKIPIF1<0的最大值為.【例2-3】（2022清遠(yuǎn)期末）若函數(shù)SKIPIF1<0的值域?yàn)镾KIPIF1<0，則實(shí)數(shù)SKIPIF1<0的取值范圍是（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0【一隅三反】1．（2022·重慶模擬）函數(shù)SKIPIF1<0定義域?yàn)椋ǎ〢．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．（2022太原）函數(shù)f(x)＝SKIPIF1<0－log2(x＋2)在區(qū)間[－1，1]上的最大值為.3．（2022云龍）已知函數(shù)y=lg（ax2﹣2x+2）的值域?yàn)镽，則實(shí)數(shù)a的取值范圍為．4．（2022陽江）函數(shù)SKIPIF1<0的值域?yàn)镽，則SKIPIF1<0的取值范圍是.5．（2022深圳期末）已知函數(shù)f(x)=ln(x2+1)，g(x)=4(m-1)sin(2x+SKIPIF1<0)-m2，若x1SKIPIF1<0∈[-1，3]，SKIPIF1<0x2∈[0，SKIPIF1<0]，f(x1)≥g(x2)，則m的取值范圍是考點(diǎn)三對數(shù)函數(shù)的性質(zhì)【例3-1】（2022高二下·東城期末）若函數(shù)SKIPIF1<0的圖象過點(diǎn)SKIPIF1<0，則SKIPIF1<0（）A．3 B．1 C．-1 D．-3【例3-2】（2022雙鴨山期末）“SKIPIF1<0”是“函數(shù)SKIPIF1<0是在SKIPIF1<0上的單調(diào)函數(shù)”的（）A．充分不必要條件 B．充要條件C．必要不充分條件 D．既不充分也不必要條件【例3-3】（2022滄州期末）已知SKIPIF1<0，則SKIPIF1<0的大小關(guān)系為（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0【例3-4】（2022·中衛(wèi)模擬）設(shè)函數(shù)f(x)=log2x，x>0log12(?x)，x<0若A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0【一隅三反】1．（2022舟山期末）已知函數(shù)SKIPIF1<0且SKIPIF1<0，則該函數(shù)圖象恒過定點(diǎn)（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．（2022懷仁期末）已知SKIPIF1<0在SKIPIF1<0上是減函數(shù)，則實(shí)數(shù)a的取值范圍是（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．（2022楊浦期末）若log12(4?x2)>A．SKIPIF1<0 B．SKIPIF1<0或SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<04．（202延慶期末）已知SKIPIF1<0，設(shè)SKIPIF1<0，則下列結(jié)論正確的是（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0考點(diǎn)四反函數(shù)及應(yīng)用【例4-1】（2022·徐匯模擬）函數(shù)SKIPIF1<0的反函數(shù)為SKIPIF1<0，則SKIPIF1<0.【例4-2】（2022·楊浦二模）函數(shù)SKIPIF1<0的反函數(shù)為.【一隅三反】1．（2022高三上·江陽期末）若函數(shù)SKIPIF1<0與SKIPIF1<0互為反函數(shù)，則SKIPIF1<0的單調(diào)遞減區(qū)間是.2．（2021蘭州期末）若函數(shù)y=SKIPIF1<0是函數(shù)SKIPIF1<0的反函數(shù)，則SKIPIF1<03（2022·青浦模擬）已知SKIPIF1<0的圖象經(jīng)過點(diǎn)SKIPIF1<0，SKIPIF1<0的反函數(shù)為SKIPIF1<0，則SKIPIF1<0的圖象必經(jīng)過點(diǎn).4．（2022高三上·楊浦模擬）已知函數(shù)SKIPIF1<0的反函數(shù)為SKIPIF1<0，則SKIPIF1<0.5（2021高三上·楊浦期中）若函數(shù)SKIPIF1<0的反函數(shù)為SKIPIF1<0，則函數(shù)SKIPIF1<0的零點(diǎn)為.6．（2021·黃浦模擬）設(shè)f﹣1（x）為函數(shù)f（x）＝log2（4x﹣1）的反函數(shù)，則當(dāng)f（x）＝2f﹣1（x）時，x的值為．8.8對數(shù)運(yùn)算及對數(shù)函數(shù)（精練）（基礎(chǔ)版）題組一題組一對數(shù)的運(yùn)算1．（2022鎮(zhèn)江月考）計(jì)算：（1）SKIPIF1<0.（2）已知SKIPIF1<0，SKIPIF1<0，求實(shí)數(shù)SKIPIF1<0的值.2．（2022上海月考）已知SKIPIF1<0，求SKIPIF1<0的值.3（2022蓮湖期中）（1）計(jì)算SKIPIF1<0；（2）若SKIPIF1<0，求SKIPIF1<0的值．4．（2021海安月考）計(jì)算：（1）SKIPIF1<0；（2）SKIPIF1<0．5．（2022高一上·中山月考）求值或化簡：（1）SKIPIF1<0；（2）SKIPIF1<0.（3）SKIPIF1<0.（4）SKIPIF1<0（5）SKIPIF1<0.（6）SKIPIF1<0.題組二題組二對數(shù)函數(shù)的三要素1．（2022·重慶模擬）函數(shù)SKIPIF1<0定義域?yàn)椋ǎ〢．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．（2022·東莞月考）函數(shù)SKIPIF1<0的定義域?yàn)椋ǎ〢．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．（2022河南）函數(shù)f(x)＝SKIPIF1<0的定義域?yàn)椋ǎ〢．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<04．（2022開封期中）已知函數(shù)SKIPIF1<0且SKIPIF1<0在區(qū)間SKIPIF1<0上的最大值與最小值的差為1，則實(shí)數(shù)SKIPIF1<0的值為（）A．2 B．4 C．SKIPIF1<0或4 D．SKIPIF1<0或25．（2022浦城）已知函數(shù)y＝log2(x2－2kx＋k)的值域?yàn)镽，則k的取值范圍是()A．0＜k＜1 B．0≤k＜1 C．k≤0或k≥1 D．k＝0或k≥1題組三題組三對數(shù)函數(shù)的性質(zhì)1．（2022高三上·西寧期末）已知SKIPIF1<0（SKIPIF1<0且SKIPIF1<0）恒過定點(diǎn)SKIPIF1<0，且點(diǎn)SKIPIF1<0在直線SKIPIF1<0（SKIPIF1<0，SKIPIF1<0）上，則SKIPIF1<0的最小值為（）A．SKIPIF1<0 B．8 C．SKIPIF1<0 D．42．（2020·新課標(biāo)Ⅱ·理）設(shè)函數(shù)SKIPIF1<0，則f(x)（）A．是偶函數(shù)，且在SKIPIF1<0單調(diào)遞增B．是奇函數(shù)，且在SKIPIF1<0單調(diào)遞減C．是偶函數(shù)，且在SKIPIF1<0單調(diào)遞增D．是奇函數(shù)，且在SKIPIF1<0單調(diào)遞減3（2022集寧月考）函數(shù)y=logSKIPIF1<0（5+4x-x2）的單調(diào)遞增區(qū)間為()A．(2,5) B．(-1,2) C．(-∞,2) D．(2,+∞)4．（2022長治期中）函數(shù)SKIPIF1<0的增區(qū)間為（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<05（2022廣東）．已知SKIPIF1<0是(?∞，＋∞)上的減函數(shù)，那么a的取值范圍是（）A．(0,1) B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<06．（2022九江開學(xué)考）函數(shù)y=SKIPIF1<0sin（SKIPIF1<0﹣2x）的一個單調(diào)遞減區(qū)間是（）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<07．（2022紹興）若函數(shù)f（x）=loga（2x2+x）（a＞0，a≠1）在區(qū)間（0，SKIPIF1<0）內(nèi)恒有f（x）＞0，則f（x）的單調(diào)遞增區(qū)間是（）A．（﹣∞，﹣SKIPIF1<0） B．SKIPIF1<0C．SKIPIF1<0 D．（0，+∞）8．（2022連城期中）函數(shù)f（x）=x3+bx2+cx+d圖象如圖，則函數(shù)SKIPIF1<0的單調(diào)遞減區(qū)間為（）A．（﹣∞，﹣2） B．[3，+∞）C．[﹣2，3] D．[SKIPIF1<0）9．（2022重慶）已知y=loga（2﹣ax）是[0，1]上的減函數(shù)，則a的取值范圍為（）A．（0，1） B．（1，2） C．（0，2） D．（2，+∞）10（2022保定期末）已知SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，則（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<011．（2022咸寧期末）已知SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，則（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<012．（2022湖北期末）已知SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，則（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<013．（2022南充期末）函數(shù)SKIPIF1<0的圖象恒過一定點(diǎn)是．14．（2022河南月考）已知函數(shù)SKIPIF1<0，則關(guān)于x的不