174 Bài tập Hàm số mũ Logarit cực hay từ đề thi đạ...

$A. (-\infty ;1) \cup (2;+\infty )$

$B. \mathrm{ℝ}\backslash \{1;2\}$

$C. y\text{'} = \frac{2x}{(x^2 +\hspace{0.17em}2)\ln 5}$

$D. \mathrm{ℝ}$

$A. D = (-\infty ;2]$

$B. D = (2;+\infty )$

$C. D = (-\infty ;2)$

$D. D = (-\infty ;+\infty )$

$A. (-\infty ;-1)$

$B. (1;+\infty )$

$C. (0;+\infty )$

$D. \mathrm{ℝ}\backslash \{\pm 1\}$

$A. (-\infty ;0]\cup [0;+\infty )$

$B. (0;2)$

$C. \mathrm{ℝ}$

$D. (-\infty ;0)\cup (2;+\infty )$

A. (2).

B. (1).

C. (3).

D. (1) và (2).

$A. D = (-\infty ;0)\cup (1;+\infty )$

$B. D = \mathrm{ℝ}\backslash \{0;1\}$

$C. D = \mathrm{ℝ}$

$D. D = (0;1)$

$A. \mathrm{ℝ}$

$B. (-\infty ;-2]$

$C. (-2;+\infty )$

$D. \mathrm{ℝ}\backslash \left\{2\right\}$

$A. \mathrm{ℝ}\backslash \{2;5\}$

$B. (2;5)$

$C. (-\infty ;2)\cup (5;+\infty )$

$D. \mathrm{ℝ}$

$A. y = {(x2 +\hspace{0.17em}1)}^{\frac{1}{2}}$

$B. y = \sqrt{x^2}$

$C. y = \frac{x}{x-1}$

$D. y = \sqrt[3]{x}$

$A. \mathrm{ℝ}\backslash \{0;2\}$

$B. (0;2)$

$C. \mathrm{ℝ}$

$D. T = (-\infty ;0)\cup (2;+\infty )$

$A. (-\infty ;0] \cup [4;+\infty )$

$B. (-\infty ;0) \cup (4;+\infty )$

$C. (0;4)$

$D. \mathrm{ℝ}\backslash \{0;4\}$

$A. y = x^{-5}$

$B. y = x^{\sqrt{2}}$

$C. y = x^{\frac{1}{3}}$

$D. y = x^{-1,7}$

$A. [3;+\infty )$

$B. (3;+\infty )$

$C. \mathrm{ℝ}\backslash \left\{3\right\}$

$D. \mathrm{ℝ}$

$A. D = \left(\frac{3}{2};+\infty \right)$

$B. D = \mathrm{ℝ}$

$C. D = (0;+\infty )$

$D. D = \mathrm{ℝ}\backslash \left\{\frac{3}{2}\right\}$

$A. (2;+\infty )$

$B. (-\infty ;2)$

$C. \mathrm{ℝ}\backslash \left\{2\right\}$

$D. \mathrm{ℝ}$

$A. D = (-\infty ;1)\cup (2;+\infty )\backslash \left\{3\right\}$

$B. D = (-\infty ;+\infty )\backslash (1;2)$

$C. D = (-\infty ;+\infty )\backslash \left\{3\right\}$

$D. D = (-\infty ;1)\cup (2;+\infty )$

$A. D = \mathrm{ℝ}$

$B. D = \mathrm{ℝ}\backslash \{-1;1\}$

$C. D = (-\infty ;-1)\cup (1;+\infty )$

$D. D = (-1;1)$

$A. \left(\frac{1}{2};2\right)$

$B. \mathrm{ℝ}\backslash \left\{\frac{1}{2}\right\}$

$C. [\frac{1}{2};+\infty )$

$D. \left(\frac{1}{2};+\infty \right)$

$A. \mathrm{ℝ}\backslash \left\{-\frac{1}{2};\frac{1}{2}\right\}$

$B. \left(-\infty ;-\frac{1}{2}\right)\cup \left(\frac{1}{2};+\infty \right)$

$C. (0;+\infty )$

$D. \mathrm{ℝ}$

$A. \mathrm{ℝ}\backslash \left\{\frac{5}{3}\right\}$

$B. \left(\frac{5}{3};+\infty \right)$

$C. [\frac{5}{3};+\infty )$

$D. \left(\frac{3}{5};+\infty \right)$

$A. \mathrm{ℝ}\backslash \{-4;1\}$

$B. \mathrm{ℝ}$

$C. [-4;1]$

$D. (-4;1)$

$A. D = (2;4)$

$B. D = (-\infty ;2)$

$C. D = (4;+\infty )$

$D. D = \mathrm{ℝ}$

$A. D = \mathrm{ℝ}\backslash \left\{-\frac{1}{2};\frac{1}{2}\right\}$

$B. D = \left(-\infty ;-\frac{1}{2}\right)\cup \left(\frac{1}{2};+\infty \right)$

$C. D\hspace{0.17em}= \mathrm{ℝ}$

$D. D = \left(-\frac{1}{2};\frac{1}{2}\right)$

$A. D = \mathrm{ℝ}\backslash \{0;2\}$

$B. D = \mathrm{ℝ}$

$A. D = (-\infty ;0)\cup (2;+\infty )$

$D. D = (0;2)$

$A. \mathrm{ℝ}\backslash \{1;2\}$

$B. (-\infty ;1)\cup (2;+\infty )$

$C. (1;2)$

$D. \mathrm{ℝ}$

$A. \mathrm{ℝ}\backslash \{-\frac{3}{2};1\}$

$B. \left(-\infty ;-\frac{3}{2}\right)\cup (1;+\infty )$

$C. \left(-\frac{3}{2};1\right)$

$D. \mathrm{ℝ}$

$A. (-\infty ;2)$

$B. (2;+\infty )$

$C. \mathrm{ℝ}$

$D. \mathrm{ℝ}\backslash \left\{2\right\}$

$A. \mathrm{ℝ}\backslash \{0;2\}$

$B. (0;2)$

$C. \mathrm{ℝ}$

$D. (-\infty ;0)\cup (2;+\infty )$

$A. f\left(x\right) = \sqrt[3]{4}$

$B. f\left(x\right) = 4^x$

$C. f\left(x\right) = e^x$

$D. f\left(x\right) = x^{\frac{1}{3}}$

$A. [1;+\infty )$

$B. \mathrm{ℝ}$

$C. (1;+\infty )$

$D. \mathrm{ℝ}\backslash \left\{1\right\}$

$A. D = [-2;\frac{3}{2})\cup (\frac{3}{2};2]$

$B. D = (-2;\frac{3}{2})\cup (\frac{3}{2};2)$

$C. D = (\frac{3}{2};2)$

$D. D = (-2;2)$

$A. (-1;2]$

$B. (-1;2)$

$C. (-\infty ;2]$

$D. [-1;2]$

$A. (1;+\infty )$

$B. [1;+\infty )$

$C. (0;+\infty )$

$D. \mathrm{ℝ}\backslash \left\{1\right\}$

$A. D = \mathrm{ℝ}\backslash \{-1;4\}$

$B. D = (-\infty ;-1]\cup [4;+\infty )$

$C. D = \mathrm{ℝ}$

$D. D = (-\infty ;-1)\cup (4;+\infty )$

$A. D = [-2;2]$

$B. \mathrm{ℝ}\backslash \{\pm 2\}$

$C. D = (-2;2)$

$D. D = (-\infty ;+\infty )$

$A. \mathrm{ℝ}\backslash \left\{\frac{5}{3}\right\}$

$B. \mathrm{ℝ}$

$C. \left(\frac{5}{3};+\infty \right)$

$D. [\frac{5}{3};+\infty )$

A. 5

B. 4

C. 7

D. 9

A. 9

B. 5

C. 6

D. 3

A. D = (-3;5]

A. D = $(-3;+\infty )\backslash \left\{5\right\}$

C. D = (-3;5)

D. D = $(-3;+\infty )$

$A. D = (-\infty ;+\infty )\backslash \left\{3\right\}$

$B. D = (-\infty ;1)\cup (2;+\infty )\backslash \left\{3\right\}$

$C. D = (-\infty ;+\infty )\backslash (1;2)$

$D. D = (-\infty ;1)\cup (2;+\infty )$

$A. \mathrm{ℝ}$

$B. \mathrm{ℝ}\backslash \{0;4\}$

$C. (-\infty ;0)\cup (4;+\infty )$

$D. (3;+\infty )$

$A. y = x^{\frac{1}{3}}$

$B. y = \ln \left|x\right|$

$C. y = x^{\frac{1}{x}}$

$D. y = \frac{1}{e^x}$

A. Tập giá trị của hàm số $y = a^x$là tập $\mathrm{ℝ}$.

B. Tập giá trị của hàm số $y = {\log }_{a}x$ là tập $\mathrm{ℝ}$. 

C. Tập xác định của hàm số $y = {\log }_{a}x$ là tập $\mathrm{ℝ}$. 

D. Tập xác định của hàm số $y = a^x$ là khoảng $(0;+\infty )$.

A. (2;5)

B. $(-\infty ;2)\cup (5;+\infty )$

C. $(-\infty ;2]\cup [5;+\infty )$

D. [2;5]

$A. D\hspace{0.17em}= (-\infty ;-1)$

$B. D\hspace{0.17em}= (1;+\infty )$

$C. D\hspace{0.17em}= (-\infty ;1)$

$D. D\hspace{0.17em}= (1;+\infty )$

$A. (3;+\infty )$

$B. (1;3)$

$C. (-\infty ;1)\cup (3;+\infty )$

$D. \mathrm{ℝ}\backslash \{1$

A. D = [0;2]

B. D = $(-\infty ;0]\cup [2;+\infty )$

C. D = $(-\infty ;0)\cup (2;+\infty )$

D. D = (0;2)

A. [0;1]

B. (0;1)

C. $(-\infty ;0]\cup [1;+\infty )$

D. $(-\infty ;0)\cup (1;+\infty )$

$A. (-\infty ;1)\cup (2;+\infty )$

$B. \mathrm{ℝ}$

$C. (0;+\infty )$

$D. (1;2)$

$A. \mathrm{ℝ}$

$B. \left(\frac{3}{2};+\infty \right)$

$C. \left(-\infty ;\frac{3}{2}\right)$

$D. (-\infty ;\frac{3}{2}]$

$A. (0;+\infty )$

$B. [0;+\infty )$

$C. \mathrm{ℝ}\backslash \left\{0\right\}$

$D. \mathrm{ℝ}$

$A. \mathrm{ℝ}$

$B. (3;+\infty )$

$C. (0;+\infty )$

$D. (2;+\infty )$

A. Trên tập xác định, hàm số đồng biến nếu a > 1, nghịch biến nếu 0 < a < 1.

B. Đồ thị hàm số có một tiệm cận đứng và không có tiệm cận ngang.

C. Tập xác định của hàm số là $\mathrm{ℝ}$.

D. Đồ thị hàm số luôn nằm bên phải trục tung.

$A. (-\infty ;0)\cup (2;+\infty )$

$B. [0;2]$

$C. (-\infty ;0]\cup [2;+\infty )$

$D. (0;2)$

$A. y = {\log }_{\sqrt{3}} x$

$B. y = {\log }_2 (\sqrt{x} + 1)$

$C. y = {\log }_{\frac{\mathrm{\pi }}{4}} x$

$D. y = {\left(\frac{\mathrm{\pi }}{3}\right)}^x$

$A. D = (0;+\infty )$

$B. D = (-1;+\infty )$

$C. D = [-1;+\infty )$

$D. D = [0;+\infty )$

A. D = [2;4]

B. D = $(-\infty ;2)\cup (4;+\infty )$

C. D = $(-\infty ;2]\cup [4;+\infty )$

D. D = (2;4)

$A. (-\infty ;1)\cup (2;+\infty )$

$B. (-\infty ;2)$

$C. (1;+\infty )$

$D. (-1;1)$

$A. (3;+\infty )$

$B. (0;3]$

$C. (0;3)$

$D. (-\infty ;0)\cup (3;+\infty )$

$A. D = \left(-\frac{3}{2};\frac{3}{2}\right)$

$B. D =(-\infty ;-\frac{3}{2}]\cup [\frac{3}{2};+\infty )$

$C. D =(-\infty ;-\frac{3}{2})\cup (\frac{3}{2};+\infty )$

$D. D = \left[-\frac{3}{2};\frac{3}{2}\right]$

$A. (1;+\infty )$

$B. (-\infty ;1)$

$C. \mathrm{ℝ}$

$D. \mathrm{ℝ}\backslash \left\{1\right\}$

$A. (-\infty ;\frac{1}{2}]\cup [2;+\infty )$

$B. (\frac{1}{2};2)$

$C. (-\infty ;\frac{1}{2})\cup (2;+\infty )$

$D. [\frac{1}{2};2]$

$A. x\ne 1$

$B. x > 1$

$C. x < 1$

$D. \forall x\in \mathrm{ℝ}$

$A. (0;1)$

$B. (-1;0)\cup (2;+\infty )$

$C. (1;+\infty )$

$D. (-\infty ;-1)$

$A. y = {\left(\frac{e}{\mathrm{\pi }}\right)}^x$

$B. y = {\left(\sqrt{2}\right)}^x$

$C. y = {\left(0,5\right)}^x$

$D. y = {\left(\frac{2}{3}\right)}^x$

$A. D = [2;+\infty )$

$B. D = \mathrm{ℝ}\backslash \left\{2\right\}$

$C. D = \mathrm{ℝ}$

$D. D = (2;+\infty )$

$A. D = \mathrm{ℝ}\backslash \left\{\frac{3}{4}\right\}$

$B. D = \mathrm{ℝ}$

$C. D = [\frac{3}{4};+\infty )$

$D. D = (\frac{3}{4};+\infty )$

$A. \left[-\frac{2}{3};1\right]$

$B. \left(-\frac{2}{3};1\right)$

$C. (-\infty ;-\frac{2}{3})\cup (1;+\infty )$

$D. (-\infty ;-\frac{2}{3}]\cup [1;+\infty )$

$A. -2\le m\le 2$

$B. m =2$

$C. m > 2 hoặc m <-2$

$D. -2 < m < 2$

$A. (-\infty ;1]\cup [2;+\infty )$

$B. [1;2]$

$C. (-\infty ;1)\cup (2;+\infty )$

$D. (1;2)$

$A. D = (-\infty ;4)\backslash \left\{0\right\}$

$B. D = (-\infty ;4)$

$C. D = (4;+\infty )$

$D. D = \left\{0\right\}\cup (4;+\infty )$

$A. D = [-3;2]$

$B. D = \mathrm{ℝ}\backslash \{-3;2\}$

$C. D = (-\infty ;-3)\cup (2;+\infty )$

$D. (-3;2)$

$A. (1;2)$

$B. (2;+\infty )$

$C. (1;+\infty )$

$D. (1;+\infty )\backslash \left\{2\right\}$

$A. (6;+\infty )$

$B. (-\infty ;6)$

$C. (0;+\infty )$

$D. (-\infty ;+\infty )$

$A. D = (-2;2)$

$B. D = (-\infty ;-2)\cup (2;+\infty )$

$C. D\hspace{0.17em}= [-2;2]$

$D. D = (-\infty ;-2]\cup [2;+\infty )$

$A. m \le \frac{1}{4}$

$B. m \ge \frac{1}{4}$

$C. m > \frac{1}{4}$

$D. m < \frac{1}{4}$

A. m > -4

B. m < 0

C. m < -4

D. m < -3

A. 4

B. 7

C. 3

D. 5

$A. {2018}^{2019}$

$B. {2019}^{2020}$

$C. {2017}^{2018}$

$D. 0$

$A. m\in \left(-\infty ;-4\right)\cup (1;+\infty )$

$B. m\in (1;+\infty )$

$A. m\in \left(-\infty ;-4\right)\cup (1;+\infty )$

$C. m\in (-\infty ;-4)$

A. (0;1)

B. $\left(\frac{1}{2};+\infty \right)$

C. $\left(0;\frac{1}{2}\right)$

D. $\left(1;+\infty \right)$

$A. (-1;4)$

$B. (-2;-1)\cup (4;+\infty )$

$C. (-2;-4)$

$D. (-4;1)\cup (2;+\infty )$

A. 2019

B. 2017

C. 2018

D. 1009

$A. D = \left(0;\frac{1}{2}\right)$

$B. D = (0;2)$

$C. D = [0;2]$

$D. D = \left[0;\frac{1}{2}\right]$

A. 2020

B. 2021

C. 2018

D. 2019

$A. x\in (-1;0)\cup (2;+\infty )$

$B. x\in (0;2)\cup (4;+\infty )$

$C. x\in (0;1)$

$D. x\in (1;+\infty )$

A. Đồ thị hàm số y = $a^x$  và đồ thị hàm số $y = {\log }_a x$ đối xứng nhau qua đường thẳng y = x.

B. Hàm số y = $a^x$  có tập xác định là $\mathrm{ℝ}$ và tập giá trị là $(0;+\infty )$.

C. Hàm số y = $a^x$ đồng biến trên tập xác định của nó khi a > 1.

D. Đồ thị hàm số  y = $a^x$ có tiệm cận đứng là trục tung.

$A. y = {\log }_3 x$

$B. y = {\log }_2 x +\hspace{0.17em}1$

$C. y = {\log }_2 (x+1)$

$D. y = {\log }_3 (x+1)$

$A. y = {(\sin x)}^3$

$B. y = 3^x$

$C. y = \sqrt[3]{x}$

$D. y = x^3$

$A. {\log }_a (x,y) = {\log }_{a}x.{\log }_{a}y; \forall x,y\in \mathrm{ℝ}$

$B. {\log }_a{x}^n = n{\log }_{a}x (\forall x > 0, n\ne 0)$

$C. {\log }_a x có nghĩa \forall x\in \mathrm{ℝ}$

$D. {\log }_{a}1 = a$

A. log (ab) = log a + log b

B. log (ab) = log a.log b

C. log $\frac{a}{b} = \frac{\log a}{\log b}$

D. log $\frac{a}{b}$= log b - log a

$A. y = {\log }_2 x$

$B. y = {\left(\frac{1}{2}\right)}^x$

$C. y = {\log }_{\frac{1}{2}} x$

$D. y = 2^x$

$A. \frac{1}{3}$

$B. \sqrt{3}$

$C. 2$

$D. \sqrt[3]{2}$

A. a < b < c

B. a < c < b

C. b < a < c

D. b > a > c

$A. 2{\log }_2\frac{a+b}{3} = {\log }_{2}a +\hspace{0.17em}{\log }_{2}b$

$B. {\log }_2\frac{a+b}{3} = 2({\log }_{2}a +\hspace{0.17em}{\log }_{2}b)$

$C. 2{\log }_2(a+b) = {\log }_{2}a +\hspace{0.17em}{\log }_{2}b$

$D. 4{\log }_2\frac{a+b}{6} = {\log }_{2}a +\hspace{0.17em}{\log }_{2}b$

$A. xy\text{'} +\hspace{0.17em}1 = -e^y$

$B. xy\text{'} +\hspace{0.17em}1 = e^y$

$C. xy\text{'} -\hspace{0.17em}1 = e^y$

$D. xy\text{'} -\hspace{0.17em}1 = -e^y$

A. a > b > c

B. b > c > a

C. b > a > c

D. c > b > a

$A. a +\hspace{0.17em}c = 2b$

$B. ac = b^2$

$C. ac = 2b^2$

$D. ac = b$

A. 2023

B. -2023

C. 2017

D. -2017

A. n = 41

B. n = 39

C. n = 49

D. n = 123

A. -2

B. 3

C. -1

D. 1

A. -3

B. -9

C. $-\frac{1}{3}$

D. $-\frac{1}{9}$