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# Warm-Up: February 1, 2013 PowerPoint PPT Presentation

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.

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

## Logarithmic Functions

Section 6.3

Part 1

### Essential Questions

• How can we convert between logarithmic and exponential forms?

### 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

## 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

### Solving for x

• Convert to exponential form

• Evaluate the exponential

### Assignment

• Page 375 #68-85