Algebra 4
Section 8-3: Logarithmic Functions
Learning Target: To write and evaluate logarithmic expressions
Standard: A2.1.A, A2.5.A, A2.5.D, A2.5.F, A2.6.B, A2.6.D
Common Core: F-IF,F-BFF-LE
1. Suppose you invest $1500 into an account that increases 5.5% each year. How
much do you have in this account after 6 years?
a. Create the exponential model: A(x) = 1500(1.055)x
b. Solve the model for 6 years: A(x) = 1500(1.055)6 = $2068.2642 = ~$2068
2. Suppose you invest $1200 at an annual interest rate of 5.5% compounded
continuously. How much money will you have in the account after five years?
a. Write the exponential function.
b. A(x) = 1200(1.055)x
This function is for compounded only once a year
c. Special exponential function
A(x) = 1200e(rt)
r = rate as decimal, t = time in years
d. A(x) = 1200e(0.055 ∙ 5) = $1579.84 = ~$1580
3. Special exponential value ex. It can be calculated on the calculator.
a. Find e3
b. Find e-2
c. Find e4/3
4. Suppose you invest $3100 at an annual interest rate of 4.3% compounded
continuously. Find the amount you will have in the account after 30 years.
5. The logarithm function: logb y = x
a. It is the inverse of an exponential function
6. Writing an exponential function in logarithmic form:
a. 103 = 1000
b. b = 10, x = 3, and y = 1000
c. log10 1000 = 3
7. Write each equation in logarithmic form:
a. 36 = 729
b. (1/2)3 = 1/8
c. 100 = 1
8. Writing a logarithmic function in exponential form:
a. log10 100 = 2
b. b = 10, x = 2, and y = 100
c. 102 = 100
9. Write each equation in exponential form:
a. log2 128 = 7
b. log6 1 = 6
c. log3 1/9 = -2
10. The common logarithm is a logarithm that uses base 10. This is the common
logarithm used on your calculator. log10 y = log y
11. Use your calculator to evaluate the common logarithmic value for the following
terms.
a. log 5
b. log (1/6)
c. log 201
12. How do you calculate log4 81
a. Use the formula: log 81 ÷ log 4 = 3.1699
b. To find the value of any logarithms: log y
log b
13. Evaluate the following logarithms:
a. log5 125
b. log8 8
c. log9 144