Properties of Logarithms

Formulas and Properties

100

What is the name of this property?

log (AB)= log(A) + log(B)

What is Product property

200

What is the name of this property?

Log_b(x/t)= log_b(x) - log_b(t)

What is Quotient property

300

Expand using the log property.

log (A/B) =

What is log A - log B

400

What is the name of this property?

log_b (u^e) = e log_b(u)

What is Power property

500

Expand using a log property:

log3(10*100)=

What is log3(10)+log3(100)

Evaluate the Log

100

Evaluate:

log₄(4) =

What is 1

200

Evaluate:

log₅(1) =

What is 0

300

Evaluate:

Log₂(64)=

What is 6

400

Evaluate:

log₅(.04) =

What is -2

500

Evaluate:

log₈(4*16)

What is Log(8)64

Expand

100

Expand:

log (4n)

What is the log 4 + log n

200

Expand:

log₅(X/25)

What is log₅(X) - log₅(25)

300

Expand:

log₂ (x/6)

What is log₂ x - log₂ 6

400

Expand:

log₇((XY)/Z)

What is log₇ x + log₇ y - log₇ z

500

Expand:

log (x⁴)

What is 4log x

Condense

100

Condense:

log x + log 5

What is Log (5x)

200

log 8 - log x

What is log (8/x)

300

Condense:

3log₂10

What is log₂(10³)

400

Condense:

log₄8 - alog₄22

What is log₄(8/22^a)

500

Condense:

log₂67 + log₂66 - log₂14

What is log₂((67*66)/14)

From Exponential to Log

100

2⁶ = 64

Log₂64 = 6

200

4¹ = 4

log₄4 = 1

300

5⁰ = 1

log₅1 = 0

400

5^-2 = .04

log₅ .04 = -2

500

3^x = 81

log₃ 81 = x