Logarithmic functions Understand logarithms and their operation rules and the change-of-base formula; know the logarithmic function, its graph, monotonicity, and its inverse relation to the exponential function.
Practice questions 1 计算： ( 1 ) ( 9 4 ) 1 2 − ( − 9.6 ) 0 − ( 27 8 ) − 2 3 + ( 3 2 ) − 2 (1)(\dfrac{9}{4})^{\frac{1}{2}}-(-9.6)^{0}-(\dfrac{27}{8})^{-\frac{2}{3}}+(\dfrac{3}{2})^{-2} ( 1 ) ( 4 9 ) 2 1 − ( − 9.6 ) 0 − ( 8 27 ) − 3 2 + ( 2 3 ) − 2 ( 2 ) lg 5 + lg 2 ⋅ lg 5 + ( lg 2 ) 2 + e ln 3 ( e (2)\lg 5+\lg 2\boldsymbol{⋅}\lg 5+(\lg 2)^{2}+e^{\ln 3}(e ( 2 ) lg 5 + lg 2 ⋅ lg 5 + ( lg 2 ) 2 + e l n 3 ( e 2 已知函数y = f ( x ) y=f(x) y = f ( x ) R R R [ 0 , + ∞ ) [0,+\infty) [ 0 , + ∞ ) m m m f ( log 3 m ) ⩾ f ( 1 ) f({{\log}_{3}}m)\geqslant f(1) f ( log 3 m ) ⩾ f ( 1 ) m m m 3 化简求值： ( 1 ) 0.064 − 1 3 − ( 1 8 ) 0 + 16 3 4 + 0.25 1 2 ( 2 ) 1 2 lg 25 + lg 2 + ( 1 3 ) log 3 2 − log 2 9 × log 3 2. (1)0.{064}^{- \frac{1}{3}}-( \dfrac{1}{8}{)}^{0}+{16}^{ \frac{3}{4}}+0.{25}^{ \frac{1}{2}} (2)\dfrac{1}{2} \lg 25+\lg 2+( \dfrac{1}{3}{)}^{{\log }_{3}2} -\log _{2}9×\log _{3}2. ( 1 ) 0. 064 − 3 1 − ( 8 1 ) 0 + 16 4 3 + 0. 25 2 1 ( 2 ) 2 1 lg 25 + lg 2 + ( 3 1 ) l o g 3 2 − log 2 9 × log 3 2. 4 已知∣ log a 3 4 ∣ < 1 |\log _{a} \dfrac {3}{4}| < 1 ∣ log a 4 3 ∣ < 1 a a a 5 下列函数中，满足f ( x 2 ) = [ f ( x ) ] 2 f(x^{2})=[f(x)]^{2} f ( x 2 ) = [ f ( x ) ] 2 ( ) () ( ) f ( x ) = ln x f(x)=\ln x f ( x ) = ln x f ( x ) = ∣ x + 1 ∣ f(x)=|x+1| f ( x ) = ∣ x + 1∣ f ( x ) = x 3 f(x)=x^{3} f ( x ) = x 3 f ( x ) = e x f(x)=e^{x} f ( x ) = e x 6 已知a a a x x x y y y ( 2 x − y e ) ⋅ ln y x = x a e \left(2x- \dfrac{y}{e}\right)·\ln \dfrac{y}{x}= \dfrac{x}{ae} ( 2 x − e y ) ⋅ ln x y = a e x a a a e e e 7 已知首项为1 1 1 { a n } \{a_{n}\} { a n } n n n S n S_{n} S n a n + 1 = 1 3 S n a_{n\text{+}1}\text{=}\dfrac{1}{3}S_{n} a n + 1 = 3 1 S n { b n } \{b_{n}\} { b n } b n = log 3 a n b_{n}\text{=}\log_{3}a_{n} b n = log 3 a n 8 若函数f ( x ) = e x − 1 x f(x)=\dfrac{e^{x-1}}{x} f ( x ) = x e x − 1 g ( x ) = x 1 + ln x g(x)=\dfrac{x}{1+\ln x} g ( x ) = 1 + ln x x x 1 x_{1} x 1 x 2 x_{2} x 2 f ( x 1 ) = g ( x 2 ) f({x}_{1})=g({x}_{2}) f ( x 1 ) = g ( x 2 ) ( ) (\quad) ( ) 9 log 27 16 log 3 4 \dfrac{\log_{27}16}{\log_{3}4} log 3 4 log 27 16 10 若10 a = 4 10^{a}=4 1 0 a = 4 10 b = 25 10^{b}=25 1 0 b = 25 ( ) (\quad) ( ) a + b = 2 a+b=2 a + b = 2 b − a = 1 b-a=1 b − a = 1 lg 20 = 1 + a 2 \lg 20=1+\dfrac{a}{2} lg 20 = 1 + 2 a b − a = 2 lg 5 2 b-a=2\lg\dfrac{5}{2} b − a = 2 lg 2 5 11 已知函数f ( x ) f\left(x\right) f ( x ) R R R f ( 0 ) = 0 f\left(0\right)=0 f ( 0 ) = 0 x > 0 x>0 x > 0 f ( x ) = log 2 ( x + 1 ) . ( 1 ) f\left(x\right)={{\log}_{2}}\left(x+1\right).(1) f ( x ) = log 2 ( x + 1 ) . ( 1 ) 12 ∀ x ∈ ( 0 , + ∞ ) ∀x\in(0,+∞) ∀ x ∈ ( 0 , + ∞ ) x e x − 3 − x − ln x ⩾ a xe^{x-3}-x-\ln x\geqslant a x e x − 3 − x − ln x ⩾ a a a a ( ) (\quad) ( ) − 2 -2 − 2 0 0 0 e − 2 − 1 e^{-2}-1 e − 2 − 1 − ln 3 -\ln 3 − ln 3 13 在y = 3 x y=3^{x} y = 3 x y = log 0.3 x y=\log _{0.3}x y = log 0.3 x y = x 3 y=x^{3} y = x 3 y = x y= \sqrt {x} y = x 0 < x 1 < x 2 < 1 0 < x_{1} < x_{2} < 1 0 < x 1 < x 2 < 1 f ( x 1 + x 2 2 ) < f ( x 1 ) + f ( x 2 ) 2 f( \dfrac {x_{1}+x_{2}}{2}) < \dfrac {f(x_{1})+f(x_{2})}{2} f ( 2 x 1 + x 2 ) < 2 f ( x 1 ) + f ( x 2 ) 14 已知函数f ( x ) = 2 x 2 − 4 x + a f(x)=2x^{2}-4x+a f ( x ) = 2 x 2 − 4 x + a g ( x ) = log a x ( a > 0 , g(x)=\log_{a}x(a>0, g ( x ) = log a x ( a > 0 , a ≠ 1 ) . ( 1 ) a≠1).(1) a = 1 ) . ( 1 ) f ( x ) f(x) f ( x ) [ − 1 , 2 m ] [-1,2m] [ − 1 , 2 m ] m m m f ( 1 ) = g ( 1 ) . f(1)=g(1).\: f ( 1 ) = g ( 1 ) . 15 已知正数x x x y y y y ln x + y ln y = e x y\ln x+y\ln y=e^{x} y ln x + y ln y = e x x y − 2 x xy-2x x y − 2 x ( ) (\quad) ( ) 1 2 ln 2 \dfrac{1}{2}\ln 2 2 1 ln 2 2 − 2 ln 2 2-2\ln 2 2 − 2 ln 2 − 1 2 ln 2 -\dfrac{1}{2}\ln 2 − 2 1 ln 2 16 下列函数中，定义域为R R R ( ) (\quad) ( ) y = 2 x y=2^{x} y = 2 x y = x ∣ x ∣ y=x|x| y = x ∣ x ∣ y = ∣ x 2 − 1 ∣ y=|x^{2}-1| y = ∣ x 2 − 1∣ y = log 2 ∣ x ∣ y=\log_{2}|x| y = log 2 ∣ x ∣ 17 设函数f ( x ) = { 2 x , x ⩽ 0 , l o g 2 x , x > 0 , f(x)=\left\{\begin{array}{l}2^{x},x\leqslant 0,\\log_{2}x,x>0,\end{array}\right. f ( x ) = { 2 x , x ⩽ 0 , l o g 2 x , x > 0 , y ∈ ( 2 , + ∞ ) y\in(2,+∞) y ∈ ( 2 , + ∞ ) x ∈ R x\in R x ∈ R 18 f（x）=㏑x+2x-5的零点一定位于以下的区间（ ） A. （1，2） B. （2，3） C. （3，4） D. （4，5） 19 x > 1 x>1 x > 1 log 1 2 ( x + 2 ) < 0 \log_{\frac{1}{2}}\left({x+2}\right)< 0 log 2 1 ( x + 2 ) < 0 ( ) (\quad) ( ) 20 计算：lg 2 + lg 5 = ( ) \lg 2+\lg 5=(\quad) lg 2 + lg 5 = ( ) − 2 -2 − 2 − 1 -1 − 1 0 0 0 1 1 1 21 已知函数f ( x ) = ln x − n x ( n > 0 ) f(x)=\ln x-nx(n > 0) f ( x ) = ln x − n x ( n > 0 ) g ( n ) g(n) g ( n ) g ( n ) − n + 2 > 0 g(n)-n+2 > 0 g ( n ) − n + 2 > 0 n n n ( 0 , 1 ) (0,1) ( 0 , 1 ) ( 0 , + ∞ ) (0,+∞) ( 0 , + ∞ ) ( 0 , 1 4 ) \left( \left. 0, \dfrac{1}{4} \right. \right) ( 0 , 4 1 ) 22 下列函数，在区间( 0 , + ∞ ) (0,+∞) ( 0 , + ∞ ) ( ) () ( ) y = ln ( x + 2 ) y=\ln (x+2) y = ln ( x + 2 ) y = − x + 1 y=- \sqrt {x+1} y = − x + 1 y = ( 1 2 ) x y=( \dfrac {1}{2})^{x} y = ( 2 1 ) x y = x + 1 x y=x+ \dfrac {1}{x} y = x + x 1 23 e ln 2 + 8 1 3 + lg 20 − lg 2 = e^{\ln 2}{+}8^{\frac{1}{3}}{+}\lg 20{-}\lg 2{=} e l n 2 + 8 3 1 + lg 20 − lg 2 = 24 已知a = 1.6 0.8 a=1.6^{0.8} a = 1. 6 0.8 b = log 3 10 b=\log_{3}10 b = log 3 10 c = sin 1 − cos 1 c=\sin 1-\cos 1 c = sin 1 − cos 1 a a a b b b c c c ( ) (\quad) ( ) a > b > c a>b>c a > b > c c > b > a c>b>a c > b > a 25 已知a = ln 2 2 a=\dfrac{\ln 2}{2} a = 2 ln 2 b = ln 3 3 b=\dfrac{\ln 3}{3} b = 3 ln 3 c = ln 6 6 c=\dfrac{\ln 6}{6} c = 6 ln 6 a a a b b b c c c ( ) (\quad) ( ) c > b > a c>b>a c > b > a 26 设a = 2020 1 2019 , b = l o g 2019 2020 , c = l o g 2020 2019 a={2020}^{ \frac{1}{2019}},b=lo{g}_{2019} \sqrt{2020},c=lo{g}_{2020} \sqrt{2019} a = 2020 2019 1 , b = l o g 2019 2020 , c = l o g 2020 2019 ( ) (\:\:\:\:) ( ) c > b > a c > b > a c > b > a 27 函数f ( x ) = ln ( x + 3 ) 1 − 2 x f(x)= \dfrac {\ln (x+3)}{ \sqrt {1-2^{x}}} f ( x ) = 1 − 2 x ln ( x + 3 ) ( ( ( ) ) ) 28 已知0 < a < b < 1 0< a< b< 1 0 < a < b < 1 c > 1 c>1 c > 1 ( ) (\quad) ( ) a c < b c ac< bc a c < b c a c > b c a^{c}>b^{c} a c > b c c a > c b \dfrac{c}{a}>\dfrac{c}{b} a c > b c log c a < log c b \log_{c}a< \log _{c}b log c a < log c b 29 已知实数a a a b b b log 2 a = log 5 b = 2 \log_{2}a=\log_{5}b=\sqrt{2} log 2 a = log 5 b = 2 lg ( ( a b ) 2 ) = \lg((ab)^{\sqrt{2}})= lg (( ab ) 2 ) = 30 方程log 2 x + x − 5 = 0 \log _{2}x+x-5=0 log 2 x + x − 5 = 0 ( ) () ( ) ( 1 , 2 ) (1,2) ( 1 , 2 ) ( 2 , 3 ) (2,3) ( 2 , 3 ) ( 3 , 4 ) (3,4) ( 3 , 4 ) ( 4 , 5 ) (4,5) ( 4 , 5 ) 31 设a = log 3 2 a={{\log }_{3}}2 a = log 3 2 b = ln 2 b=\ln 2 b = ln 2 c = 5 − 1 2 c={{5}^{-\frac{1}{2}}} c = 5 − 2 1 ( ) () ( ) c < b < a c < b < a c < b < a b < c < a b < c < a b < c < a c < a < b c < a < b c < a < b 32 已知函数f ( x ) = 1 − 2 2 a x − 1 + 1 ( a > 0 f(x)=1- \dfrac {2}{2a^{x-1}+1}(a > 0 f ( x ) = 1 − 2 a x − 1 + 1 2 ( a > 0 a ≠ 1 ) a\neq 1) a = 1 ) R R R ( ( ( ) ) ) a a a ( ( ( ) ) ) f ( x ) f(x) f ( x ) 33 与函数y = x y=x y = x ( ) () ( ) y = x 2 y= \sqrt {x^{2}} y = x 2 y = ( x ) 2 y=( \sqrt {x})^{2} y = ( x ) 2 y = x 2 x y= \dfrac {x^{2}}{x} y = x x 2 y = log a a x ( a > 0 且 a ≠ 1 ) y=\log _{a}a^{x}(a > 0{且}a\neq 1) y = log a a x ( a > 0 且 a = 1 ) 34 已知集合A = { x ∣ y = − x 2 − x + 2 } , B = { x ∣ ln x < 1 } , A=\left\{ x\left|y=\sqrt{-{{x}^{2}}-x+2}\right.\right\},B=\left\{ x\left|\ln x< {{1}_{{}}}\right.\right\}, A = { x y = − x 2 − x + 2 } , B = { x ∣ ln x < 1 } , A ∩ B = ( ) A\cap B=(\quad) A ∩ B = ( ) 35 已知a = log 3 6 a=\log _{3}6 a = log 3 6 b = 1 + 3 − log 3 e b=1+3\;^{-\log _{3}e} b = 1 + 3 − l o g 3 e c = ( 2 3 ) − 1 c=( \dfrac {2}{3})^{-1} c = ( 3 2 ) − 1 a a a b b b c c c ( ) () ( ) a > b > c a > b > c a > b > c 36 设函数f ( x ) = a x − a x − 2 ln x f(x)=ax- \dfrac {a}{x}-2\ln x f ( x ) = a x − x a − 2 ln x f ( x ) f(x) f ( x ) x = 2 x=2 x = 2 a a a f ( x ) f(x) f ( x ) f ( x ) f(x) f ( x ) a a a 37 已知函数f ( x ) = ln x x − a ( a ∈ R ) . ( 1 ) f\left(x\right)=\dfrac{{\rm\ln}x}{x}-a\left(a\in R\right).(1) f ( x ) = x ln x − a ( a ∈ R ) . ( 1 ) f ( x ) f(x) f ( x ) a a a f ( x ) f(x) f ( x ) m m m 38 函数y = log 1 3 ( x 2 − 9 ) y=\log \;_{ \frac {1}{3}}(x^{2}-9) y = log 3 1 ( x 2 − 9 ) ( ) () ( ) ( − ∞ , 0 ) (-∞,0) ( − ∞ , 0 ) ( − ∞ , − 3 ) (-∞,-3) ( − ∞ , − 3 ) ( 3 , + ∞ ) (3,+∞) ( 3 , + ∞ ) ( − 3 , 0 ) (-3,0) ( − 3 , 0 ) 39 已知函数f ( x ) = ln ( x + x 2 + 1 ) + 1 f(x)=\ln(x+\sqrt{{{x}^{2}}+1})+1 f ( x ) = ln ( x + x 2 + 1 ) + 1 a , b a\text{ },\text{ }b a , b f ( 4 a ) + f ( b − 1 ) = 2 f(4a)+f(b-1)=2 f ( 4 a ) + f ( b − 1 ) = 2 1 a + 1 b \dfrac{1}{a}+\dfrac{1}{b} a 1 + b 1 40 规定两数a a a b b b ( a , b ) (a,b) ( a , b ) a c = b a^{c}=b a c = b ( a , b ) = c (a,b)=c ( a , b ) = c 2 3 = 8 2^{3}=8 2 3 = 8 ( 2 , 8 ) = 3 (2,8)=3 ( 2 , 8 ) = 3 ( 3 , 27 ) = (3,27)= ( 3 , 27 ) = 41 对于下列结论： ① \text{①} ① y = a x + 2 ( x ∈ R ) y\text{=}a^{x\text{+}2}(x{\in}R) y = a x + 2 ( x ∈ R ) y = a x ( a > 0 y\text{=}a^{x}(a\text{ > }0 y = a x ( a > 0 a ≠ 1 ) a\neq 1) a = 1 ) ② \text{②} ② 42 已知函数f ( x ) = log 4 x − 1 x + 1 ( 1 ) f\left(x\right)={{\log}_{4}}\dfrac{x-1}{x+1}(1) f ( x ) = log 4 x + 1 x − 1 ( 1 ) f ( a ) = 1 2 f\left(a\right)=\dfrac{1}{2} f ( a ) = 2 1 a a a f ( x ) f\left(x\right) f ( x ) 43 函数y = log 2 ( x + 1 x − 1 + 5 ) ( x > 1 ) y=\log_{2}(x+\dfrac{1}{x-1}+5)(x>1) y = log 2 ( x + x − 1 1 + 5 ) ( x > 1 ) ( ) (\quad) ( ) 4 4 4 − 4 -4 − 4 − 3 -3 − 3 3 3 3 44 已知1 ∣ sin α ∣ = − 1 sin α \dfrac{1}{|\sin \:α|} =- \dfrac{1}{\sin \:α} ∣ sin α ∣ 1 = − sin α 1 lg ( cos α ) \lg (\cos \:α) lg ( cos α ) α α α α α α M ( 3 5 , m ) M( \dfrac{3}{5} , m) M ( 5 3 , m ) 45 若a > b > 1 , 0 < c < 1 a > b > 1,0 < c < 1 a > b > 1 , 0 < c < 1 ( ) () ( ) a c > b c {{a}^{c}} > {{b}^{c}} a c > b c a b c < b a c a{{b}^{c}} < b{{a}^{c}} a b c < b a c log a c > log b c {{\log }_{a}}c > {{\log }_{b}}c log a c > log b c 46 设函数
f ( x ) = { 2 e x − 1 , x < 2 log 3 ( x 2 − 1 ) , x ⩾ 2 f(x)=\left\{\begin{align}&2{{e}^{x-1}},x< 2\\ &{{\log}_{3}}\left({{x}^{2}}-1\right),x\geqslant 2\\\end{align}\right. f ( x ) = { 2 e x − 1 , x < 2 log 3 ( x 2 − 1 ) , x ⩾ 2 … 47 （1）求值：( 3 ) 2 + 16 3 4 + ( 3 − 1 ) 0 (\sqrt[] { 3 }) ^ { 2 } +16 ^ { \frac { 3 } { 4 } } +(\sqrt[] { 3 }-1) ^ { 0 } ( 3 ) 2 + 1 6 4 3 + ( 3 − 1 ) 0 l g 25 + l g 4 + 5 l o g 5 2 + l o g 3 27 { \rm{ l } }{ \rm{ g } }25+{ \rm{ l } }{ \rm{ g } }4+5 ^ { { \rm{ l } }{ \rm{ o } }{ \rm{ g } }_{ 5 } 2 } +{ \rm{ l } }{ \rm{ o } }{ \rm{ g } }_{ 3 } \sqrt[] { 27 } l g 25 + l g 4 + 5 l o g 5 2 + l o g 3 27 48 若集合A = { x ∣ log 1 2 x ⩾ 1 2 } A=\{x|\log _{ \frac {1}{2}}x\geqslant \dfrac {1}{2}\} A = { x ∣ log 2 1 x ⩾ 2 1 } ∁ R A = ( ) ∁_{R}A=() ∁ R A = ( ) ( − ∞ , 0 ] ∪ ( 2 2 (-∞,0]∪( \dfrac { \sqrt {2}}{2} ( − ∞ , 0 ] ∪ ( 2 2 + ∞ ) +∞) + ∞ ) 49 使式子log ( 2 x − 1 ) ( 2 − x ) {\log}_{(2x-1)}(2-x) log ( 2 x − 1 ) ( 2 − x ) x x x ( ) (\quad) ( ) x > 2 x>2 x > 2 x < 2 x< 2 x < 2 1 2 < x < 2 \dfrac{1}{2}< x< 2 2 1 < x < 2 1 2 < x < 2 \dfrac{1}{2}< x< 2 2 1 < x < 2 50 已知函数f ( x ) = a x 2 + x ln x + x f(x)=ax^{2}+x\ln x+x f ( x ) = a x 2 + x ln x + x a = 1 a=1 a = 1 f ( x ) f(x) f ( x ) ( 1 , f ( 1 ) ) (1,f(1)) ( 1 , f ( 1 )) a = − e a=-e a = − e ∣ f ( x ) ∣ − ln x = 1 2 x |f(x)|-\ln x= \dfrac {1}{2}x ∣ f ( x ) ∣ − ln x = 2 1 x 51 已知函数f ( x ) = { ln x , x > 0 x 2 + 2 x , x ⩽ 0 f(x)=\left\{\begin{array}{l}\ln x,x>0\\ {x}^{2}+2x,x⩽0\end{array}\right. f ( x ) = { ln x , x > 0 x 2 + 2 x , x ⩽ 0 g ( x ) = f ( x ) + 1 g(x)=f(x)+1 g ( x ) = f ( x ) + 1 52 已知a = 3 0.5 a=3^{0.5} a = 3 0.5 b = log 3 2 b=\log_{3}2 b = log 3 2 c = tan 2 π 3 c=\tan\dfrac{2π}{3} c = tan 3 2 π ( ) (\quad) ( ) a > b > c a>b>c a > b > c b > a > c b>a>c b > a > c c > a > b c>a>b c > a > b a > c > b a>c>b a > c > b 53 16 16 16 17 17 17 54 定义在R R R f ( x ) f(x) f ( x ) ( 0 , + ∞ ) (0,+∞) ( 0 , + ∞ ) f ( 1 3 ) = 0 f\left(\dfrac{1}{3}\right)=0 f ( 3 1 ) = 0 f ( log 1 8 x ) > 0 f\left({{\log}_{\frac{1}{8}}}x\right)>0 f ( log 8 1 x ) > 0 x x x 55 命题p p p ∀ x ∈ [ 1 , 2 ] ∀x\in[1,2] ∀ x ∈ [ 1 , 2 ] 2 x 2 − x − m > 0 2x^{2}-x-m>0 2 x 2 − x − m > 0 q q q ∃ x 0 ∈ [ 1 , 2 ] ∃x_{0}\in[1,2] ∃ x 0 ∈ [ 1 , 2 ] log 2 x 0 + m > 0 \log_{2}x_{0}+m>0 log 2 x 0 + m > 0 p ∧ q p∧q p ∧ q m m m 56 已知命题p p p ∣ x − 1 ∣ + ∣ x + 2 ∣ > m |x-1|+|x+2|>m ∣ x − 1∣ + ∣ x + 2∣ > m R R R q q q f ( x ) = log ( 5 − 2 m ) x f(x)=\log_{(5-2m)}x f ( x ) = log ( 5 − 2 m ) x ¬ p ¬p ¬ p ¬ q ¬q ¬ q ( ) (\quad) ( ) 57 已知函数f ( x ) = ( log 2 x ) 2 − log 2 x 2 + 3 f\left(x\right)={\left({\log }_{2}x\right)}^{2}-{\log }_{2}{x}^{2}+3 f ( x ) = ( log 2 x ) 2 − log 2 x 2 + 3 x ∈ [ 1 , 4 ] x∈\left[1,4\right] x ∈ [ 1 , 4 ] f ( x ) f\left(x\right) f ( x ) 58 设a a a b b b a > b > 1 a>b>1 a > b > 1 log 2 a > log 2 b > 0 \log_{2}a>\log_{2}b>0 log 2 a > log 2 b > 0 ( ) (\quad) ( ) 59 已知直线y = a x + b ( a ∈ R , b > 0 ) y=ax+b(a\in R,b>0) y = a x + b ( a ∈ R , b > 0 ) f ( x ) = e x f(x)=e^{x} f ( x ) = e x g ( x ) = ln x + 2 g(x)=\ln x+2 g ( x ) = ln x + 2 a + b a+b a + b ( ) (\quad) ( ) e + 2 e+2 e + 2 3 3 3 e + 1 e+1 e + 1 60 设函数f ( x ) = − 4 x + 2 x + 1 − 1 f(x)=-4^{x}+2^{x+1}-1 f ( x ) = − 4 x + 2 x + 1 − 1 g ( x ) = lg ( a x 2 − 4 x + 1 ) g(x)=\lg(ax^{2}-4x+1) g ( x ) = lg ( a x 2 − 4 x + 1 ) x 1 ∈ R x_{1}\in R x 1 ∈ R x 2 ∈ R x_{2}\in R x 2 ∈ R f ( x 1 ) = g ( x 2 ) f(x_{1})=g(x_{2}) f ( x 1 ) = g ( x 2 ) a a a