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Logarithmic Functions
2
Logarithmic Functions
Real Life scenario
To measure a student’s retention of
knowledge, the student is tested after a given amount
of time. A student’s score on an Algebra 2 test t months after the school year is over can be approximated by
, where y(t) is the student’s score as a
percent.
a. What was the student’s score at the time the
school year ended (t = 0)?
b. What was the student’s score after 3 months?
c. What was the student’s score after 15 months?
Power Property of Logarithms
How do logarithmic functions work?
Other Helpful properties
Quotient Property of Logarithms
Pg. 475
What are Logarithmic Functions?
Logarithms have properties that are helpful when solving three main properties are Product property, Quotient property and Power property. They are also able to be written in exponential form and exponential forms are able to be written in logarithmic. For it to be written in exponential you can just move y to be the exponent for b ,the base and move the x to the other side of the equal sign. And to evaluate logarithms you can just equal the logarithmic expression they give you to x and then you could just solve for x.
Product Property of Logarithms
Video
A Logarithmic Function is represented by
and its also considered the inverse of exponential functions. which is represented by y=b^x.
Example 3
Solve the equation. Check the solution.
Example 1
STEPS
Write the equation in logaritmic form.
STEPS
Solution
Pg. 490
Solution
Example 2
evaluate the expression.
pg. 474
STEPS
Solution
Pg. 474
Melissa Hernandez
Real Life Scenario Steps and Solutions
a.
c.
The student's score after 15 months will be a 61
The student's score at the time the school year ended will be a 85
b.
(3+1)
The student's score after 3 months will be a 73
Why is it the most FUN of all?
Why are Logarithmic Functions Important?
Logarithmic functions are the most fun of all the other concepts because they are easier and simpler, since they have three main properties that can help solve exponential functions.
Logarithmic functions are important because of their relationship to exponential functions. They can be used to solve exponential equations and to explore properties of exponential and logarithmic. They are also very valuable in calculus, where they will be used to calculate the slope of certain functions,etc. In addition, they contibute to economics, like exponential, they have to deal with investment growth, and other things.