Properties of Logarithms

Formulas and Properties

100

What Property? 

log (AB)=

What is the product property

200

What property?

Log(x/t)=

What is the quotient property

300

Expand.

log A/B=

What is log A - log B

400

What property?

log a^b=

What is the power property

500

Expand.

log₃(10*100)=

What is log₃(10)+log₃(100)

Evaluate the Log

100

log₄4=

What is 1

200

log₅1=

What is 0

300

Log₂64=

What is 6

400

log₅.04=

What is -2

500

log₄(1/16)

What is -2

Expanding with Properties

100

Log (4n)

What is the Log 4 + Log n

200

Log₅(3X²/25)

What is log 3+ 2 log₅(X) - log₅(25)

300

Log₂(x/6)

What is Log₂ x - Log₂ 6

400

Log (X³Y)/Z⁴)

What is (3 Log x + Log y) - 4 Log z

500

Log (8xy³)

What is Log 8+ log x +3 log y

Condense with Properties

100

Log X + Log 5

What is Log (5X)

200

Log 8 - Log X

What is Log (8/X)

300

Log₂x^1/2

What is 1/2 Log₂ x

400

Log₄8 - (Log₄2+ 3 log₄ x)

What is Log₄ 8/2x³

500

2 (Log x + Log 3)- 3 log y

What is Log (3x)²/y³

From Exponential to Log

100

2⁶=64

Log₂64=6

200

log₄4=1

4¹=4

300

5⁰=1

log₅1=0

400

5^-2=.04

log₅.04=-2

500

3^x=81

log₃81=x