Scholarship Precalculus Name__________________ Logs and

Scholarship Precalculus
Name__________________
Logs and Exponentials Worksheet
(3.1 – 3.3)
Convert each exponential into its logarithmic form:
1. 93  729
2. 25 
4
1
1
3.   
16
2
1
32
Convert each log into its exponential form:
4. log10 100  2
5. log 2 64  6
6. log x z  y
Evaluate each log.
7. log 2 8
8. log 4 8
9. log 3
1
9
Use the properties of logs to expand each logarithm.
10. log3
3
6
x
 x  3
11. ln 

 xy 
Use the properties of logs to condense each of the following to one logarithm.
1
1
12. ln x  ln y
13. log8  x  4   7log8 y
4
3
Evaluate each of the following. Use properties of logs to combine into one log and then convert into
exponential form. Do not use calculators! Show your work!
14. log3 45  log3 6  log3 10
15. log6 4  2log6 3
16.
1
log3 144  2log3 6
2
17. 2  log2 20  log2 5
18. Let b be a number such that logb 3  1.5 and logb 5  2.2 . Evaluate each of the following.
b) logb 3b2
a) logb 45
c) logb
 3
3
7
Solve for x using the one-to-one property for exponentials and logarithms. Show your work!
1
19. 3x2 
20. e5 x 7  e15
21. log4  x  7   log4 14
9
1
1
23. log x  log8  log81
3
2
22. log7 x  2log7 6  log7 4
x
x
1
1
24. Use the graph of f ( x )    to describe the transformations needed to graph g ( x )      2 .
2
2
What is the domain, range, and y-intercept of the graph?
25. Sketch the graph of the function log  x  5  4 .
What is the domain, range, and x-intercept of the graph ?

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