Free Printable Exponential and Logarithmic Equations Quiz

1.

1. Write each exponential equation in logarithmic form.
$4^{3x}=11$

a)

$\log_411=3x$

b)

$\log_43x=11$

c)

$\log_{3x}4=11$

d)

$\log_{11}3x=4$

2.

2. Write the exponential equation in logarithmic form.

$8^{x-1}=33$

a)

$\log_3x-1=8$

b)

$\log_83=x-1$

c)

$\log_38=x-1$

d)

$\log_8x-1=3$

3.

3. Write the exponential equation in logarithmic form.
$e^{2x}=7$

a)

$\ln7=2x$

b)

$\ln2x=7$

c)

$\log2x=7$

d)

$\log7=2x$

4.

4. Write the exponential equation in logarithmic form.

$13=2^{5x}$

a)

$\log_{13}5x=2$

b)

$\log_{5x}2=13$

c)

$\log_213=5x$

d)

$\log_25x=13$

5.

5. Write the logarithmic equation in exponential form.
$\log_5x=9$

a)

$9^x=5$

b)

$5^9=x$

c)

$9^x=5$

d)

$9^5=x$

6.

6. Write the logarithmic equation in exponential form.
$\log2x=-3$

a)

$10^{-3}=2x$

b)

$10^{2x}=-3$

c)

$2x^{-3}=10$

d)

- $-3^{2x}=10$

7.

7. Write the logarithmic equation in exponential form.
$6=\log_3(x+5)$

a)

$x+5=3^6$

b)

$3=\left(x+5\right)^6$

c)

$6=3^{\left(x+5\right)}$

d)

$x+5=6^3$

8.

8. Write the logarithmic equation in exponential form.
$\ln(4x)=2$

a)

$e^2=4x$

b)

$e^{4x}=2$

c)

$\log4x=2$

d)

$\log2=4x$

9.

9. Evaluate the expression without a calculator.
$\log_381$

(a)

10.

10. Evaluate the expression without a calculator.

$\ln e^{-5}$

(a)

11.

11. Evaluate the expression without a calculator.

$\log\frac{1}{100}$

(a)

12.

12. Evaluate the expression without a calculator.
$\log_981$

(a)

13.

13. Evaluate the expression without a calculator.

$\log_4\frac{1}{16}$

(a)

14.

14. Evaluate the expression without a calculator.

$\log10$

(a)

15.

15. Evaluate the expression without a calculator.

$\log_{36}\frac{1}{6}$

(a)

16.

16. Evaluate the expression without a calculator.

$\ln\frac{1}{e^4}$

(a)

17.

17. Use the table to find $f\left(g\left(2\right)\right)$ , if possible.

(a)

18.

18. Use the table to find $h(-1)$ , if possible.

(a)

19.

19. Use the table to find $h(0)$ , if possible.

(a)

20.

20. Use the table to find $g^{-1}(-6)$ , if possible.

(a)

21.

21. Use the table to find $g^{-1}(0)$ , if possible.

(a)

22.

22. Use the table to find $f^{-1}(7)$ , if possible.

(a)

23.

23. Use the table to find $f(g^{-1}(2))$ , if possible.

(a)

24.

24. Use the table to find $g(f^{-1}(-6))$ , if possible.

(a)

25.

25. Use the table to find $f^{-1}(g^{-1}(-4)),$ if possible.

(a)

26.

26. $f\left(f\left(4\right)\right)$

(a)

27.

27. $g\left(5\right)$

(a)

28.

28. $g\left(g\left(6\right)\right)$

(a)

29.

30. $g\left(10\right)$

(a)

30.

29. $\left(f^{-1}\circ f^{-1}\right)\left(2\right)$

(a)

31.

31. $f\left(f\left(-3\right)\right)$

(a)

32.

32. What is the minimum value of g(x)?

(a)

33.

33. What is the maximum value of g(x)?

(a)

34.

34. What is the domain of $f^{-1}$ ?

a)

[-4,7]

b)

[-5,12]

c)

[-4,12]

d)

[-5,7]

35.

35. What is the range of $f^{-1}$ ?

a)

[-4,7]

b)

[-5,12]

c)

[-4,12]

d)

[-5,7]

36.

36. What is the maximum value of g?

a)

1/5

b)

1/4

c)

4

d)

5

37.

37. What is the value of $f\left(h^{-1}(2)\right)$ ?

a)

-5

b)

-4

c)

-3

d)

-2

38.

38. What is the value of $h^{-1}\left(g\left(3\right)\right)$ ?

a)

-6

b)

-5

c)

-4

d)

-3

39.

39. What is the value of $g\left(g\left(2\right)\right)$ ?

a)

1/2

b)

2

c)

3

d)

4

40.

40. Let $k\left(x\right)=3x-7$ . Which of the following is an expression for $k^{-1}\left(x\right)$

a)

$7x+3$

b)

$\frac{1}{3}x+7$

c)

$3\left(x+7\right)$

d)

$\frac{1}{3}\left(x+7\right)$

41.

Let $p\left(x\right)=\frac{2x+3}{x-5}$ . Which of the following is an expression for $p^{-1}\left(x\right)$

a)

$\frac{8}{x-2}$

b)

$\frac{5x-3}{x+2}$

c)

$\frac{5x+3}{x-2}$

d)

$\frac{x+5}{2x-3}$

Exponential and Logarithmic Equations Quiz

Total questions: 41

Worksheet time: 10hrs 15mins

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