LAWS OF LOGARITHMS

SECTION 5.6

Why do we need the Laws?

To condense and expand logarithms:

To Simplify!

LAWS OF LOGARITHMS

3 3 3log 5 log log 5x x

4 4 4

9log 9 log logx

x

When you are adding logs multiply!!

When you are subtracting logs divide!!

1.

2.

LAWS OF LOGARITHMS

3log 3logx x3.

3log 3logx x

LAWS OF LOGARITHMS

5log5 x x4.

The log and exponential are inverses of each otherso they cancel each other!

Example:

3log 23 x 2x ln5e 5

LAWS OF LOGARITHMS

8log 8x x5.

This is because

And

8log 8x

So we get 8log 8x

8log 8 1

Let’s Practice! (No Calculator)

log3 log 6 log5

12 122log 6 log 4

Evaluate

Let’s Practice! (No Calculator)

1log 64 2log5

3

1ln

2x

e

Evaluate

Simplify

Let’s Practice! (No Calculator)

3ln xe

4

1lne

Let’s Practice! (No Calculator)

4 log510

Express y in terms of x:

log 5logy x

Express y in terms of x:

ln 3ln 2ln 6y x

Write as a single logarithm:

82 log x

Solve:

7 7log 8 log 2 2x

Solve:

24 4 4log 2 log log 8x x

Homework:

5.6 Page 2001-45 every other odd