Log Properties

Product Rule

100

log_a(xy) = 

log_ax + log_ay

200

Expand so that there are two logs

log₅(7•8)

log₅7 + log₅8

300

Simplify the expression so that there is one log

log₉12 + log₉9

log₉108

400

Given the log below, write out all of its possible expanded forms

log₃64

log₃1 + log₃64

log₃2 + log₃32

log₃4 + log₃16

log₃8 + log₃8

Quotient Rule

100

log_a(x/y) =  

log_ax - log_ay

200

Expand so that there are two logs

log₆(8/4)

log₆8 - log₆4

300

Simplify the expression so that there is one log

log₁₁125 - log₁₁5

log₁₁(125/5) = log₁₁25

400

If the simplified version of a log came out to be log₆3, list 3 possibilities for the original expression. 

log₆6 - log₆2 

log₆18 - log₆6

log₆36 - log₆12

Power Rule

100

log_ax^p = 

p log_ax

200

Rewrite using log properties

log₂y⁴

4 log₂y

300

Rewrite using log properties

6 ln(a)

ln(a⁶)

400

Rewrite using log properties

log₈((3x)⁴)

4 log₈3 + 4 log₈x 

Change of Base Rule

100

log_ax = 

log_bx / log_ba

200

Rewrite using log properties

log₄7

log 7 / log 4

(any base works)

300

Rewrite using log properties

log 17 / log 5

log₅17

400

Rewrite using log properties

log₁₂9

log 9 / log 12

True or False

100

log₅7² = 7log₅2

FALSE

--> 2log₅7

200

log₅(6) + log₅(12) = log₅(72) 

TRUE

6•12 = 72

300

log₇(14) - log₇(2) = log₇(7)

TRUE

14/2 = 7

400

log₃10 = log 10 / log₃3

FALSE

--> new base needs to be the same