5.5 Prop of Logarithms

[Pages:3]Precalculus 5.5 Properties of Logarithms

Objective: able to work with the properties of logs; expand a log expression as a sum/difference; condense a log expression to a single log; evaluate/graph logs for any base

Logarithms have some very useful properties that can be derived directly from the definition and the laws of exponents.

Complete the following properties of logarithms:

1. loga 1 =

2. loga a =

3.

a

log a

M

=

4. loga a r =

5. loga (MN) =

6. loga (M + N) =

7. loga (M ? N) =

8.

=

9.

=

10. loga (M r) =

Prove two of the preceding properties.

Logarithms can be used to transform products into sums, quotients into differences, and powers to factors.

1. Write

as a sum and / or difference of logarithms, and express powers as factors.

2. Write 21

+

9-

2 5 as a single logarithm.

To calculate logarithms having a base other than 10 or e, you use the change of base formula.

If a 1, b 1, and M are positive real numbers, then

= !"#$ , and

!"#$

= !"# , & = 10 , and

!"#

= !"#$ , & = ( .

!"#$

Calculate to the thousandths place.

3. log5 18

4. ) 2

5. Graph * = +

If M, N, and a are positive real numbers, with a 1, then the following is true: M = N if and only if loga M = loga N.

This means that we can `take the log of both sides' of an equation, which we will do in the next section.

I have no clue what to do even if somebody is

explaining the problem to me 1

What do I still need to work on?

Rate yourself on how well you understood this lesson.

I can do it if someone is

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walking me through the

own, but I need the help of

I can do it on my own

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my notes/textbook

2

3

4

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