Algebra 2
Module 15 and 16 Review
Name: ______________________________________________________________Date:_________________________Hour: ____
15.1 Defining and Evaluating Logarithmic Functions
Write each exponential equation in logarithmic form.
1.
37 = 2187
2.
122 = 144
3.
53 = 125
Write each logarithmic equation in exponential form.
4.
log10 100,000 = 5
5.
log4 1024 = 5
6. log9 729 = 3
Evaluate each expression without using a calculator.
7.
log 1,000,000
8.
log 10
9.
log 1
10.
log4 16
11.
log8 1
12.
log5 625
13. Given 𝑓(𝑥) = 2𝑥 , complete the following:
a) Find the inverse function
b) Find the domain and range of the inverse function.
c) Determine the end behavior of the inverse function.
d) Identify the asymptote , any intercepts and at least two other points and use these to graph the
inverse.
14. The acidity level, or pH, of a liquid is given by the formula pH  log
1
, where [H+] is the
[H ]
concentration (in moles per liter) of hydrogen ions in the liquid. The hydrogen ion concentration in
moles per liter for a certain brand of tomato vegetable juice is 0.000316. Find its pH level.
Module 15 and 16 Review
Algebra 2
Evaluate each by writing the logarithmic equation as an exponential equation with common
bases on each side.
1
15. If 𝑓(𝑥) = 𝑙𝑜𝑔3 𝑥, find 𝑓(243), 𝑓 (27), and 𝑓(√27)
1
3
16. If 𝑓(𝑥) = 𝑙𝑜𝑔1 𝑥, find 𝑓 (64) , 𝑓(256), and 𝑓( √16)
4
15.2 Graphing Logarithmic Functions
Given each function, tell the transformations that have been applied to the graph of the parent
function. Then, identify the function’s asymptote, reference point, and at least one other point to
sketch the graph. Give the domain and range in set notation.
1. 𝑔(𝑥) = 𝑙𝑜𝑔2 𝑥 + 4
2. 𝑔(𝑥) = 3𝑙𝑜𝑔4 (𝑥 + 6)
3. 𝑓(𝑥) = −log(𝑥 + 5)
4. 𝑓(𝑥) = ln 𝑥 + 3
Algebra 2
Module 15 and 16 Review
16.1 Properties of Logarithms
Express each as a single logarithm. Simplify, if possible.
1. log3 9 + log3 27
2. log2 8 + log2 16
3. log10 80 + log10 125
4. log6 8 + log6 27
5. log3 6 + log3 13.5
6. log4 32 + log4 128
7. log2 80 - log2 10
8. log10 4000 - log10 40
9. log4 384 - log4 6
10. log2 1920 - log2 30
11. log3 486 - log3 2
12. log6 180 - log6 5
Expand each logarithm.
13. 𝑙𝑛√𝑥
14. log (3x)6
15. 𝑙𝑜𝑔𝑏 (𝑥 2 √𝑦)
16. 𝑙𝑜𝑔6 (36𝑦4 )
3
√𝑥
Simplify, if possible.
17. log4 46
18. log5 5 x + 5
19. 7log7 30
20. 12log12 1
21. log8 85
22. log3 94
Use the Change of Base Property to Evaluate. Round to the nearest hundredth.
19. log12 1
20. log3 30
21. log5 10
Module 15 and 16 Review
Algebra 2
22.
The Richter magnitude of an earthquake, M, is related to the energy released in ergs, E, by the
2
 E 
. Find the energy released by an earthquake of magnitude 4.2.
11.8 
 10

formula M  log 
3
16.2 Solving Exponential Equations
Solve each equation algebraically. Round to the nearest thousandth, if necessary.
1.
52 x  20
 1
 
x
2. 122 x8  15
 1 
2x
3. 2x6  4
 1 
x 6
4.    162
2
5.    64
 32 
6.  
 27 
7. 6e10 x 8  4  34
8. 8 10 
9. 6e4 x 1  3  37
7 x 6
 8  59
 27
10. In 2004, the population of a small farming community was 8500 and has been declining at a rate
of 7% per year.
a) Write an exponential function to model the population of the town.
b) When will the population be less than 6000?