Logarithms

Evaluating Logs with Calculator

100

log₇49

x = 2

200

log₃27

x = 3

300

log₂64

x = 6

400

log₆₄4

x = 1/3

500

log₉1/81

x = -2

Evaluating Logs for X

100

log₂16 = x

x = 4

200

log₃(6x - 9) = 3

x=6

300

log₄(14 + 6x) = 2

x = 1/3

400

log₃(x+5) +6 = 10 

x = 76

500

log₃(5x + 2) = log₃(7x - 8)

x = 5

Change of Base Formula Equations

100

log₁₆64

x = 3/2

200

log₈32

x = 5/3

300

log₂54

Round to the nearest hundredth

x = 5.75

400

log₁₀294

Round to the nearest hundredth

x = 2.47

500

log₆1/36

x = -2

Converting Logs to Exponential

100

log₃9 = 2

3² = 9

200

log₆216 = 3

6³ = 216

300

log₇1 = 0

7⁰ = 1

400

log₉27 = 3/2

9^3/2 = 27

500

log₄1/16 = -2

4^-2 = 1/16

Properties of Logs

100

What is this property rule?

logM/N = log_aM - log_aN

Quotient Property

200

What is this property rule?

log_aMN = log_aM + log_aN

Product Property

300

What is this property rule?

log_a Mⁿ = n log_aM

Power Rule

400

What is this property rule?

log_aM = log_bM/log_bN

Change of Base Rule