Log Properties

R U FINISHED?

1

Complete the following:

log₂ xy = log₂ x + _?_

log₂ y

2

Complete the following:

log₇ (28/3) =  _?_  -  log₇ 3

log₇ 28

3

Complete the following:

2log x + 3log y = _?_

log x²y³

4

Complete the following:

log₆ x + log₆ y - log₆ z = ?

log₆ (xy/z)

CHANGE ME!

1

Evaluate using the change of base formula.

Round to the nearest thousandth.

log₃7

1.771

2

Evaluate using the change of base formula.

Round to the nearest thousandth.

log₈ 2

.333

3

Evaluate using the change of base formula.

Round to the nearest thousandth.

log₆ 1/2

-.387

4

Evaluate using the change of base formula.

Round to the nearest thousandth.

log_1/2 42

-5.392

GIVE ME PROPS

1

Expand:

 log (7/32)

log 7 - log 32

2

Condense:       

log₄ x + 3log₄ y

log₄ xy³

3

Expand:

log₅ 7x²y^-3

log₅ 7 + 2log₅ x - 3log₅ y

4

Condense:

log 4 - 2log x + 1/2log y

log 4y^1/2/x²

TRANSLATE PLEASE!

1

State the asymptote for:   

y = log (x - 7) + 3

x = 7

2

State the asymptote for:

y = log (x) - 4

x = 0

3

State the transformations for y = log₃ (x + 5) - 3

when compared to its parent function y = log₃ x

Shift

left 5 units 

and

down 3 units

4

State the transformations for y = -log₄ (x - 5) when

compared to its parent function y = log₄ x

Shift

right 5 units 

reflects across the x-axis

EVALUATE ME

1

Use log properties to evaluate:

log₃ 45 - log₃ 5

2

2

Use log properties to evaluate:

log₂ 4 + log₂ 8 

5

3

Use log properties to evaluate:

log₆ 9 + log₆ 8 - log₆ 2

2

4

Use log properties to evaluate:

3log₉ 3 - log₉ 9

1/2