Calculus
Unit One: Assignment #5
Exponential and Logarithmic Functions
Write each of the following in logarithmic form.
1. 43 = 64
2. 27 1/3 = 3
3. 3x = 19
4. x5 = 125
5. 37 = x
Write each of the following in exponential form.
6. log 5 625 = 4
7. log 27 9 = 2/3
8. log x 5 = 20
9. log 10 13 = x
10. log 7 x = 4.2
Use properties of exponents to solve each of the following equations for x.
11. 2 2x + 1 = 4
12. 5 1 – 2x = 1/5
13. 2x·8-x = 4x
Use properties of logarithms to write each of the following as a single logarithm.
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Use property #5 to solve the following equations for x.
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Calculus
Unit One: Assignment #5
Exponential and Logarithmic Functions
Write an equation of an exponential function that goes through the given pair of points.
23. (3, 12) and (14, 100)
24. (5, 50) and (8, 10)
Solve each of the following problems related to half-life and doubling time.
25. The half-life of a certain radioactive substance is 12 days. If there are 10.32 grams initially, write
an equation to determine the amount, A, of the substance as a function of time.
a. When will the substance be reduced to 1 gram?
b. By what percent is the substance decaying by each day?
26. The doubling time of the price of a certain commodity is 18 years. If the commodity originally
was priced at $4.67 in 2000, write an equation to determine the price, P, of the substance as a
function of time.
a. When will the commodity cost $6.00?
b. By what percent is the commodity increasing by each year?
27. The value of a home rose from $125,000 in 2003 to $130,000 in 2009. Write an equation to
determine the value, V, of the home as a function of time.
a. What is the doubling time of the value of the home?
b. By what percent is the value of the home increasing by each year?
c. When will the home have a value of $150,000?
Determine the domain of each of the following logarithmic functions.
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