Logarithmic Functions and Exponential Equations
Unit 8
[7-3 in text]
Logarithmic Functions
Today’s Objective:
I can write and evaluate logarithmic expressions.
Solving exponential equations using common bases
Write each side with
the same base.
Since bases are the same
exponents must be equal.
Exponential & Logarithm Equations
Exponential
Equation
Inverse
Logarithm
Equation
Exponent/power
Base
Result
Common Log
:
Logs with a base 10
Written log only – no base # needed
Calculator button: [LOG]
Read: log base
b
of
a
Solving using logs –
any
base
Write in
logarithmic form
Write in
exponential form
Solve each equation by using common
base method
Find the inverse of each function
Earthquakes
Richter Scale (magnitude)
Intensity Level (Measured on seismometers
In December 2004 an earthquake with magnitude 9.3 on the
Richter scale hit off the northwest coast of Sumatra.
How many times more intense was the December
earthquake from the March quake?
Earthquakes
In this unit, learn how to write and evaluate logarithmic expressions, solve exponential equations using common bases, work with exponential and logarithm equations, understand logarithmic form, and find the inverse of functions. Practice solving equations with various bases and learn to convert between exponential and logarithmic forms effectively.
Download Presentation
Please find below an Image/Link to download the presentation.
The content on the website is provided AS IS for your information and personal use only. It may not be sold, licensed, or shared on other websites without obtaining consent from the author.If you encounter any issues during the download, it is possible that the publisher has removed the file from their server.
You are allowed to download the files provided on this website for personal or commercial use, subject to the condition that they are used lawfully. All files are the property of their respective owners.
The content on the website is provided AS IS for your information and personal use only. It may not be sold, licensed, or shared on other websites without obtaining consent from the author.
E N D
Presentation Transcript
Unit 8 [7-3 in text] Logarithmic Functions Today s Objective: I can write and evaluate logarithmic expressions.
Solving exponential equations using common bases 4?= 32 1 16 5?= 125 4?= 2? 5 Write each side with the same base. 2 = 2 1 4?= 2? = 5 ? =5 42 3 5?= 5 2 4?= 4 2 Since bases are the same exponents must be equal. 2?= 7 ? = 2 ? = 3
Exponential & Logarithm Equations Exponential Equation Logarithm Equation Inverse ?log??= ? Exponent/power a = x b = x logb a log???= ? Base Result Common Log: Logs with a base 10 Written log only no base # needed Calculator button: [LOG] Read: log base b of a
? = ?? log?? = ? Write in logarithmic form Write in exponential form 14 = 5? ? log log514 = ? 514 log38 = ? 3 3?= 8 23 = ?? log?23 = ? 52?= 34 log534 = 2? log8(6) + 1 = ? 6 = 103?+1 log106 = 3? + 1 log86 = ? 1 8? 1= 6 log6 = 3? + 1
Solve each equation by using common base method ? = ?? log?? = ? log464 = 2? + 3 ? = log5625 log327 = ? 7 3? 7= 27 42?+3= 64 42?+3= 43 5?= 625 3? 7= 33 5?= 54 2? + 3 = 3 ? 7 = 3 ? = 4 ? = 0 ? = 10
Find the inverse of each function ? = ?? log?? = ? ? = 5log7(? + 4) ? =3? ? = 34?+ 2 4 ? = 5log7(? + 4) ? 5= log7(? + 4) ? = 34?+ 2 ? =3? ? 2 = 34? 4 log3(? 2) = 4? ? 5= ? + 4 4? = 3? 7 log3(? 2) 4 ? 5 4 = ? = ? log34? = ? 7
