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Warm-Up: February 1, 2013

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- 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

- How can we convert between logarithmic and exponential forms?

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

- Evaluate each of the following logarithms:
- A) log525
- B) log28
- C) log381

- Evaluate each of the following logarithms

- pH scale in chemistry
- Decibels – noise levels
- Richter scale – earthquake strength
- Apparent magnitude (brightness) of a star
- Musical intervals – semitones

Exponential formLogarithmic form

103 = 10003 = log101000

Exponent

Base

Move the base to the other side of the equation

- 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”

- Convert to Logarithmic form

- Convert to Logarithmic form

- Convert to Exponential Form

- Convert to Exponential Form

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

- Solve v=log100.001

- Solve v=log41

- Page 374 #12-35, 56-67

- Evaluate the following logarithms

Logarithmic Functions

Section 6.3

Part 2

- How can we solve logarithmic equations?

- Evaluate the logarithm
- We did this last class

- Convert to exponential form
- Use a radical or fractional exponent to isolate b
- Remember b>0

- Convert to exponential form
- Evaluate the exponential

- Page 375 #68-85