MATH1050: Logarithmic Equations
Instructor: Laura Strube
Name
Student ID :
Answer the questions in the spaces provided or copy the questions neatly on
our own paper.
Solve the following equations for x. For each of the logarithm equations answer the three
following questions:
• What is the implied domain of this equation? (Use interval notation)
• What are the potential solutions?
• What is the actual solution?
1. (5 points) What are the 4 logarithmic rules we discussed in class?
• Rule 1
• Rule 2
• Rule 3
• Rule 4
2. (5 points) (a) What is the change of base formula?
(b) Why is it important?
3. (5 points) What steps are not mentioned in the textbook, but must be done for every
logarithmic function equations?
4. (5 points) ln(x2 ) = 4
5. (5 points) log(x) = 2
6. (5 points) log(x2 − x) + log(2) − log(x) = 1
Page 2
7. (5 points) log(x2 ) + 1 = log(3x + 1)
8. (5 points) logπ (x) = 2
9. (5 points) log7 (2x + 3) = log7 (x) = log7 (2)
Page 3
10. (5 points) log5 (5x ) = 2x − 1
11. (5 points) log2 (3x − 2) − log2 (x2 ) = 0
12. (5 points) log4 (x2 − 9) − log4 (x + 3) = 3
Page 4
13. (5 points) log2 (logx 16) = 2
14. (5 points) ln(x2 − 4) + log3 (x2 − 4) = 1
15. (5 points) ln(x2 ) − 15 = log(x2 ) This is not a typo!
Page 5
16. (5 points) ln(ex ) + eln(x) + ln(e) = 4
17. (5 points) log(x2 ) − log(x2 − 4) + log(x) = log(x − 1)
18. (5 points) log[(x + 5)(x − 1)] − log(x + 3) = log(x − 1)
Page 6