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Warm-Up: February 1, 2013. The population of India was 952,108,100 in 1996 and was growing at a rate of 1.3% per year. Write the expression that would predict the population in 2000. Write the expression that would predict the population in 2010. Homework Questions?. Logarithmic Functions.

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Warm up february 1 2013
Warm-Up: February 1, 2013

  • The population of India was 952,108,100 in 1996 and was growing at a rate of 1.3% per year.

  • Write the expression that would predict the population in 2000.

  • Write the expression that would predict the population in 2010



Logarithmic functions

Logarithmic Functions

Section 6.3

Part 1


Essential questions
Essential Questions

  • How can we convert between logarithmic and exponential forms?



Logarithm
Logarithm

  • The logarithm of a number to a certain base is the exponent to which the base must be raised to equal the number.


Example 1
Example 1

  • Evaluate each of the following logarithms:

  • A) log525

  • B) log28

  • C) log381


You try 1
You-Try #1

  • Evaluate each of the following logarithms


Use of logarithms don t copy
Use of Logarithms (don’t copy)

  • pH scale in chemistry

  • Decibels – noise levels

  • Richter scale – earthquake strength

  • Apparent magnitude (brightness) of a star

  • Musical intervals – semitones


Converting forms
Converting Forms

Exponential form Logarithmic form

103 = 10003 = log101000

Exponent

Base

Move the base to the other side of the equation


Converting forms1
Converting Forms

  • You can take the log (with same base) of both sides

  • Or you can make both sides exponents with the same base.

  • Logs and exponents of the same base “cancel”


Example 2
Example 2

  • Convert to Logarithmic form


You try 2
You-Try #2

  • Convert to Logarithmic form


Example 3
Example 3

  • Convert to Exponential Form


You try 3
You-Try #3

  • Convert to Exponential Form


Evaluating logarithms
Evaluating Logarithms

  • To evaluate a logbx, ask yourself, “b to what exponent gives me x?”


Example 4 solve
Example 4: Solve

  • Solve v=log100.001


You try 4 solve
You-Try #4: Solve

  • Solve v=log41


Assignment
Assignment

  • Page 374 #12-35, 56-67


Warm up february 4 2013
Warm-Up: February 4, 2013

  • Evaluate the following logarithms



Logarithmic functions1

Logarithmic Functions

Section 6.3

Part 2


Essential question
Essential Question

  • How can we solve logarithmic equations?


Solving for y
Solving for y

  • Evaluate the logarithm

  • We did this last class


Solving for b
Solving for b

  • Convert to exponential form

  • Use a radical or fractional exponent to isolate b

  • Remember b>0




Solving for x
Solving for x

  • Convert to exponential form

  • Evaluate the exponential




Assignment1
Assignment

  • Page 375 #68-85


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