6.11 Notes – Change of base and log equations

209814

6.11 Notes ² Change of base

and log equations

Objectives:

1) Use common logs to solve equations.

2) Apply the change of base formula.

1)

332log log 9x

2)

772log log 83x

3)

6 6 62log log 4 log 64x

4)

8 8 8log 48 log log 4y

5)

3 3 3log 5log 2 log 8x

6)

2 2 2log (3 14) log 5 log 2uu

7) ln( 3) ln ln4xx 8)

2ln4 ln lnxe

9) 2

553log ( 9) 6 log 1x

Solve Logarithm equations by applying log properties:

480/81

Day 11

Notes Why would we ever want to change the base of our logarithm? Well, the reason is that we cannot evaluate a logarithm like _________________ in our heads.

Change of Base Formula:

logac

Examples:

1)

4log 25

2)

3log 18

3)

6log 5

State your answer as an exact answer and then approximate your answer to the nearest thousandths. 1) 3 27x 2)

5 120x

3) 52xe
4)

24 27x

5)

42 82x

6)

2342xe

7)

35 72x

8) 34 10
x e

Change of base formula:

Use logs to solve exponential equations:

6.11 Notes ² Change of base

and log equations

Objectives:

1) Use common logs to solve equations.

2) Apply the change of base formula.

1)

332log log 9x

2)

772log log 83x

3)

6 6 62log log 4 log 64x

4)

8 8 8log 48 log log 4y

5)

3 3 3log 5log 2 log 8x

6)

2 2 2log (3 14) log 5 log 2uu

7) ln( 3) ln ln4xx 8)

2ln4 ln lnxe

9) 2

553log ( 9) 6 log 1x

Solve Logarithm equations by applying log properties:

480/81

Day 11

Notes Why would we ever want to change the base of our logarithm? Well, the reason is that we cannot evaluate a logarithm like _________________ in our heads.

Change of Base Formula:

logac

Examples:

1)

4log 25

2)

3log 18

3)

6log 5

State your answer as an exact answer and then approximate your answer to the nearest thousandths. 1) 3 27x 2)

5 120x

3) 52xe
4)

24 27x

5)

42 82x

6)

2342xe

7)

35 72x

8) 34 10
x e

Change of base formula:

Use logs to solve exponential equations: