Logarithms and Graphs
Name:____________
Wells Worksheet (W2)
Date:
1.
Block:
Evaluate log25(5) without a calculator. Make sure to explain the process.
Exercises 2-7, write the equation in exponential form. If possible, check to make sure it works.
2. log3 27=3
3. log 4 256  4
4.
log 6 36  2
5.
log x 216  3
6.
log 2 x  3
7.
log8 y  x
Exercises 8-13, write the equation in logarithmic form.
8. 35  243
9.
10. 4 1 
1
4
100.12  1.318
11. 16
1
2

1
4
12. 4 x  64
13. 13 y  x
Exercises 14-17, solve the equation for x.
14. log10 100000  x
15. log5 x  3
16. log x 1024  5
17. log6  x  1  3
Logarithms and Graphs
Name:____________
Since you do not know how to evaluate a logarithm statement directly, producing a logarithm graph
directly is a difficult task. One way to graph a logarithm function is to consider the graph’s inverse:
an exponential equation. Keep this in mind as you complete 18-30.
18. Use f  x   2x to answer the following questions.
a. Complete the table below for f  x  .
X
Y
-5
-4
-3
-2
-1
b. Complete the table for the inverse, f 1  x  .
X
Y
c. Graph f 1  x  on the axes below.
d. What logarithmic function represents f 1  x  ?
0
1
2
3
4
Logarithms and Graphs
Name:____________
19. Use y  log1 2  x  to answer the following questions.
a. What exponential equation represents the inverse of y ?
b. Complete the table below for inverse of y .
x
y
-4
-3
-2
-1
c. Complete the table for y  log1 2  x  .
x
y
d. Graph y  log1 2  x  on the axes below.
0
1
2
3
4
5
Logarithms and Graphs
Name:____________
20. Use g  x   log5  x  to answer the following questions.
a. What exponential equation represents g 1  x  ?
b. Complete the table below for g 1  x  .
x
y
-4
-3
-2
c. Complete the table for g  x  .
x
y
d. Graph g  x  on the axes below.
-1
0
1
2
3
4
5
Logarithms and Graphs
Name:____________
21. Use y   14  to answer the following questions.
x
a. Complete the table below for y   14  .
x
x
y
-5
-4
-3
-2
-1
0
b. Complete the table for the inverse of y .
x
y
c. Graph the inverse of y on the axes below.
d. What logarithmic function represents the inverse of y ?
1
2
3
4
Logarithms and Graphs
Name:____________
Answer the following questions with the help of the previous exercises.
22. Describe the general shape of the logarithm graph.
23. Explain how the logarithm graph is related to the exponential graph.
24. When the base of the logarithmic function is between 0 and 1, what happens to the value of y as x
increases?
25. When the base of the logarithmic function is greater than 1, what happens to the value of y as x
increases?
26. What is the domain of the logarithm graph?
27. What is the range of the logarithm graph?
28. What was always the x-intercept of our logarithm graphs? Why is this always the case?
29. What is the equation for the vertical asymptote for all of our logarithm graphs?
30. Would y  log1  x  be a function? Use the exponential inverse to help explain why/why not.