Graphing Logarithmic Functions
Properties of Logarithms, (Condensing & Expanding)
Solving Logarithmic Equations
Applications of Logs and Exponentials
Nonlinear Regression
100
The domain of
f(x)=log_3(x-2)+4
What is x > 2?
100
Condense the logarithm:
5logx+7logy
What is
log(x^5y^7)
100
Solve:
log_3x=5
What is x = 243?
100
Margaret invested $2000 at an annual interest rate of 4%, compounded continuously. If she does not make any withdrawals or deposits, approximately how much money will she have after 5 years?
What is $2,442.81?
100
What is used to determine the best model for a set of data?
What is "r" - The correlation coefficient?
200
The asymptote of f(x)=log(x+2)-1
What is
x=-2?
200
Expand the logarithm:
log_5(x^2y)
What is
2log_5x+log_5y
200
Solve:
ln4+ln(x-1)=0
What is x = 5/4?
200
In a murky lake, the intensity of light is reduced by 5% for every meter that the light travels below the surface of the water. What percent of the original light intensity remains at a depth of 2 meters below the surface?
What is 90.25%?
200
The population of Austin, Texas was 346,000 in 1980, 466,000 in 1990, 567,000 in 2000, 806,000 in 2010, and 951,000 in 2017. Find an exponential regression model that can predict Austin's population x years since 1980. Round to the nearest thousandth.
What is
y=345,749.642(1.028)^x
300
The transformations of f(x)=log(x-4)+5
What are 4 units to the right and 5 units up?
300
Expand the logarithm:
log(m^5n^3)^2
What is
10logm+6logn
300
Solve:
log_4(x-8)+log_4(x+4)=3
What is x = 12?
300
In an experiment investigating the growth of spores in varying soil conditions, a certain spore colony grew an average of 3 times larger during each 24-hour period. If the colony contained 50 spores at the beginning of the experiment, how many spores were there at the end of the 4th day?
What is 4050 spores?
300
Students performed an experiment to test how long a bowl of soup can sit out in the culinary arts kitchen before reaching an unsafe food storage temperature. They found that the bowl of soup took 1 minute to reach a temperature of 190oF, 3 minutes to cool to 170oF, 8 minutes to reach 130oF, and 10 minutes to reach 120oF. Use logarithmic regression to formulate an equation that models the data. Round to the nearest thousandth.
What is
y=194.713-30.809lnx
400
The decreasing interval of
f(x)=-ln(x+5)
What is
(-5,oo)
400
Condense the logarithm:
4log_7a+(5log_7a-3log_7a)
What is
log_7(a^9/b^3)
400
Solve:
-3*4^(2y+9)+11=-4
What is y = -3.9196?
400
A biologist predicts that the height of a certain tree will increase exponentially with time, tripling every 60 years. The tree is now 5 meters tall. According to the biologist's prediction, in how many years would the tree become 45 meters tall?
What is 120 years?
400
The data below represents the length and mid-shaft diameters of the humerus bones of African Antelopes. Using a power regression equation, what mid-shaft diameter will correspond to a length of 305.7 mm?
What is 47 mm?
500
The end behavior of
f(x)=log_(1/3)(x+1)-2
What is 
500
Expand the logarithm:
log_3((4x)/y)^2
What is
log_3(16)+2log_3x-2log_3y
500
Solve:
8^(2k+3)=6^(3k-1)
What is k = 6.6015?
500
The function below models the average number of free throws a basketball player can make consecutively during practice as a function of time, where x is the number of consecutive days the basketball player has practiced for two hours. After how many days of practice can the basketball player make an average of 6 consecutive free throws?
f(x)=1+1.5ln(x+1)
What is 28 days?
500
A student purchased a used car for $8500. Two years later it was valued at $6000. After 6 years, the car was valued at $3000. Find an exponential regression equation and answer the following question. If the student wants to sell the car when it reaches a value of $2,000, how long will the student own the car before selling it?
What is 8.35 years?