Basic Logarithm Properties

Exponential to Log

100

5⁴ = 125, where 5 is called the...

Base

200

4⁶ = 4096, where the 6 is represented by the letter....

x

300

The equation for turning a logarithm into an exponential is....

b^x = a

400

Write 2³ = 8 as a logarithm.

log₂8 = 3

500

Write 6² = 36 as a logarithm.

log₆36 = 2

Log to Exponential

100

Write the following in exponential form: log_ba = x

b^x = a

200

Write the following in exponential form: log₅25 = 2

5² =25

300

Write the following in exponential form: log 3 = 1000

10³ = 1000

400

Write the following in exponential form: log₈48 = x

8^x = 48

500

Write as an exponential then solve for x:

log₇ x = 5

16807

Product Rule

100

What symbol should go here:

log_bmn = log_bm ________ log_bn

+

200

Condense: log 4 + log 8 

log 32

300

Condense: log₂ 7 + log₂ 6

log₂ 42

400

Condense: log₇5 + log₇x

log₇5x

500

Condense: log₃ x + log₃ 6x²

log₃ 6x³

Quotient Rule

100

What symbol should go here:

log_b m/n = log_b m ________ log_b n

-

200

Condense: log₂ 8 - log₂ 2

log₂ 4

300

Condense: log₈ 21 - log₈ 3

log₈ 7

400

Condense: log x - log 3

log (x/3)

500

Condense: log₄ x³ - log₄ 3x⁴

log₄ (1/3x)

Power Rule

100

If I say "3 to the power of 4 (3⁴)," 4 could also be called the .....

exponent

200

Expand: log₅3²

2 log₅3

300

Condense: 4 log 8

log 8⁴

400

Expand: log₉7⁴

4 log₉ 7

500

Condense: 

1/2 log8x

log sqrt(8x)

Random

100

The base of a log if it is not written is...

10

200

No matter the base, log 1 will always equal....

0

300

To use any of the log properties that we have learned, your logs must have what in common?

bases

400

Tell me the change of base formula.

log_ba = log a / lob b

500

SOLVE: (I want a number answer, it will be a decimal)

4log₃2

2.524