Warm-Up: Simplify each of the following

24.0

25.-3

26.3

27.-2

28.Ask for graphs

29.Ask for graphs

Homework Solutions

• Do you guys remember the natural base?– e

• Well just like there is a natural base, there is a natural log as well.– that is the natural log and the notation for that is ln– The natural log and natural base are inverses of each other

Natural Logarithm

• How to find using our calculator.– In TI-84, hit ALPHA, WINDOW and there is an option to insert a log

with a base other than 10.– For TI-83, use the change of base formula in your calculator

– When given – You can also do

• Now find

Calculator Exploration

Both yields the same answer

Properties of Logarithms

• Work in pairs to complete the handout.

• It is ok if you don’t finish it all when we go over it, just work on what you can.

Properties of Logarithms Exploration

1b).

2b).

1a).

2a).

Product Property

General Rule

1b).

2b).

1a).

2a).

Quotient Property

General Rule

1b).

2b).

1a).

2a).

Power Property

General Rule

• Remember how I told you yesterday that logarithms are the inverse of exponentials.

• Also remember I told you another way to read logarithms is “the log is the exponent”

• Well I want you to notice something:– When you have you add the exponents.– When you have you subtract the exponent.– When you have you multiply the exponents.

Remember…

log 4 𝑥5Example 1: Expand the expression

ln3 𝑦 4

𝑥3

Example 2: Expand the expression

Worksheet #26

Homework