1. Warm Up
Jasmine receives a 3.5% raise at the end of each year from her employer to account for inflation. When she started working for the company in 1994, she was earning a salary of $31,000.
A. What was Jasmine’s salary in 2000 and 2004?
B. If Jasmine continues to receive a raise at the end of each year, how much money will she earn during her final year if she plans on retiring in 2024?
Find the inverse of : 𝑓 𝑥 = 2 𝑥 and 𝑔 𝑥 = 10 𝑥

2. Logarithmic Functions

3. More than a Knot on a Log The inverse of 𝑓 𝑥 = 𝑏 𝑥 is:
Some common logarithmic scales:
Richter scale
Decibel scale pH

4. A Convertible!!!
Convert the following from logarithmic form to exponential form or vice verse. Afterwards, solve for the given variable.
1. log =𝑥 𝑦 = 5
3. log =𝑥 𝑦 =2
5. log 8 𝑥 = log =𝑦

5. Basic properties you noticed
log 𝑏 1 =
log 𝑏 𝑏 =
log 𝑏 𝑏 𝑥 =
𝑏 log 𝑏 𝑏 𝑥 =

6. That which is common and natural
Common logarithm
Natural logarithm
𝑙𝑜𝑔1= 𝑙𝑛1=
𝑙𝑜𝑔10= 𝑙𝑛𝑒=
𝑙𝑜𝑔 10 𝑥 = 𝑙𝑛 𝑒 𝑥 =
10 𝑙𝑜𝑔𝑥 = 𝑒 𝑙𝑛𝑥 =

7. Your evaluation Evaluate the following: (try it without a calculator)
1. log ln 𝑒 0.73
log ln⁡(−5)
5. log 𝑒 ln 6
7. log − ln 1 𝑒 3

8. Can you hear me now?
The intensity level of a sound, measured in decibels, can be modeled by 𝑑 𝑤 =10 log 𝑤 𝑤 0 , where w is the intensity of the sound in watts per square meter and 𝑤 0 is the constant 1.0∗ 10 −12 watts per square meter.
1. If the intensity of the sound of a person talking loudly is 3.16∗ 10 −8 watts per square meter, what is the intensity level of the sound in decibels?
2. If the threshold of hearing for a certain person with hearing loss is 5 decibels, will a sound with an intensity level of 2.1∗ 10 −12 watts per square meter be audible to that person?

9. Can you hear me now?
The intensity level of a sound, measured in decibels, can be modeled by 𝑑 𝑤 =10 log 𝑤 𝑤 0 , where w is the intensity of the sound in watts per square meter and 𝑤 0 is the constant 1.0∗ 10 −12 watts per square meter.
3. Sounds in excess of 85 decibels can cause hearing damage. Determine the intensity of a sound with an intensity level of 85 decibels.

10. Sketch the graph of 𝑓 𝑥 = log 3 𝑥 , and then provide the listed information.
Domain:
Range:
Intercepts:
Asymptotes:
End behavior:
Increasing or decreasing?

11. Sketch the graph of 𝑓 𝑥 = log 1 2 𝑥 , and then provide the listed information.
Domain:
Range:
Intercepts:
Asymptotes:
End behavior:
Increasing or decreasing?

12. For each of the above, list:
Domain, Range, intercept, extrema, asymptote, end behavior, and continuity.