Properties of Logarithms

Section 8.5

WHAT YOU WILL LEARN:

1. How to use the properties of logarithms to simplify and evaluate expressions.

Some Questions

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?

?

43

2

7

34

x

x

x

xx

• How do you simplify the following:

So…..

vuuv bbb logloglog

vuv

ubbb logloglog

Remember that logarithms are another way to write exponents.

The Properties of Logarithms are based on the properties of exponents –

Product Property:

Quotient Property:

Power Property: unu bn

b loglog

Using Properties of Logarithms

209.17log

683.03log

5

5

Use to approximate the

following:

1.

2. log521

3. log549

7

3log5

You Try!

091.111log

732.05log

9

9

• Use to approximate the following:

1.

2. log955

3. log925

11

5log5

Expanding a Logarithmic Expression

y

x32

7log• Expand . Assume x and y are

positive.

You Try!

65 2log x• Expand . Assume x and y are

positive.

Condensing a Logarithmic Expressions• Condense log 6 + 2 log 2 – log 3

You Try!

x33 log57log2 • Condense

Change of Base Formula

c

uuc log

loglog

c

uuc ln

lnlog and

Example• Evaluate the expression log37 using common and

natural logarithms.

1. log37

2. log37

Homework

page 496, 14-24 even, 30-42 even, 46-52 even, 58, 60, 70