Solve Exponential and Logarithmic Equations

Questions on solving exponential and logarithmic equations and ,indirectly, on all properties of exponential and logarithmic functions are presented. These questions may be used as a self test.

If you prefer to go through a tutorial before the test, Go here.

A set of 10 questions are presented in this page. More questions can be accessed through the applet below.

Solve Exponential and Logarithmic Equations, questions with answers

Select the right answer.

Question 1: Find all real solutions to the logarithmic equation.

ln (x) = 2


a: 2

b: 2
e

c: 1 , 0

d: no real solutions

e: e
2

Question 2: Find all real solutions to the exponential equation.

e x = 6


a: 6

b: 6 / e

c: ln (6)

d: e
6

e: no real solutions

Question 3: Find all real solutions to the logarithmic equation.

ln (x) + ln (2) = 3


a: no real solutions

b: e
3 / 2

c: e
3 / ln (2)

d: 3
e / 2

e: 3 / ln (2)

Question 4: Find all real solutions to the exponential equation.

e 3x = -1


a: no real solutions

b: ln (-1) / 3

c: -1 / ln (3)

d: 0

e: e
-1 , 3



Question 5: Find all real solutions to the exponential equation.

e 2x - 3e x + 2 = 0


a: 1 , 2

b: e , e
2

c: no real solutions

d: 0 , ln (2)

e: e
2

Question 6: Find all real solutions to the logarithmic equation.

ln (x + 1) + ln (x) = ln (2)


a: 1 , -2

b: 0 , ln (-2)

c: e , e
2

d: -2

e: 1

Question 7: Find all real solutions to the logarithmic equation.

ln (x + 1) - ln (x) = 2


a: 1

b: e
2

c: 1 / (e
2 - 1)

d: 1 / (ln (2) - 1)

e: no real solutions

Question 8: Find all real solutions to the logarithmic equation.

ln (x 2 - 1) - ln (x - 1) = ln (4)


a: [ 1 + sqrt(17) ] / 2 , [ 1 - sqrt(17) ] / 2

b: -2 , 3

c: no real solutions

d: ln (3)

e: 3



Question 9: Find all real solutions to the exponential equation.

e 2x e 3x - 3 = 2


a: ln (5) / 5

b: no real solutions

c: 1

d: -1 , 1

e: ln (5)

Question 10: Find all real solutions to the logarithmic equation.

ln (x 4) + ln (x 2) - ln (x 3) - 2 = 7


a: 9
1/3

b: e
3

c: 1

d: no real solutions

e: 0

More Questions with Answers - Applet

Once you finish the applet self test, you can review your answers and change them if necessary. You can also compare them to the right answers.

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1 - click on the button above "click here to start" and MAXIMIZE the window obtained.

2 - click on "start" on the main menu.

3 - answer the question by checking a,b,c,d or e in the lower part of the window.

You can review your answers and change them by checking the desired letter. Once you have finished, press "finish" and you get a table with your answers and the right answers to compare with.


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