Warm up february 1 2013
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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

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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

Section 6.3

Part 1


Essential Questions

  • How can we convert between logarithmic and exponential forms?


One-to-One Property of Exponents


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

  • Evaluate each of the following logarithms:

  • A) log525

  • B) log28

  • C) log381


You-Try #1

  • Evaluate each of the following logarithms


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

Exponential formLogarithmic form

103 = 10003 = log101000

Exponent

Base

Move the base to the other side of the equation


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

  • Convert to Logarithmic form


You-Try #2

  • Convert to Logarithmic form


Example 3

  • Convert to Exponential Form


You-Try #3

  • Convert to Exponential Form


Evaluating Logarithms

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


Example 4: Solve

  • Solve v=log100.001


You-Try #4: Solve

  • Solve v=log41


Assignment

  • Page 374 #12-35, 56-67


Warm-Up: February 4, 2013

  • Evaluate the following logarithms


Homework Questions?


Logarithmic Functions

Section 6.3

Part 2


Essential Question

  • How can we solve logarithmic equations?


Solving for y

  • Evaluate the logarithm

  • We did this last class


Solving for b

  • Convert to exponential form

  • Use a radical or fractional exponent to isolate b

  • Remember b>0


Example 5 – Solve for b


You-Try #5 – Solve for b


Solving for x

  • Convert to exponential form

  • Evaluate the exponential


Example 6 – Solve for x


You-Try #6 – Solve for x


Assignment

  • Page 375 #68-85


  • Login