From Exponents to Logs

Fill in the blanks and empty cells for each table below. The first row of each table has been completed for you.

Find the Related Logarithmic or Exponential Statement

	Exponential Equation	Logarithmic Equation
Example:	5³ = 125	log₅ 125 = 3
1	9² = 81
2		log₂ 32 = 5
3	x^y = z
4		log_a b = c

Exponential Equation

Logarithmic Equation

Example:

5³ = 125

log₅ 125 = 3

9² = 81

log₂ 32 = 5

x^y = z

log_a b = c

Phrasing 1

	Expressions	Translation	Evaluates to:
Example:	log₂(1)	"To get 1, I raise 2 to what power?"	0
5	log₂(8)	"To get 8, I raise 2 to what power?"
6	log₅(25)	"To get , I raise to what power?"
7	log₅(1)	"To get , I raise to what power?"
8		"To get 81, I raise 3 to what power?"
9	log₄(1)

Expressions

Translation

Evaluates to:

Example:

log₂(1)

"To get 1, I raise 2 to what power?"

log₂(8)

"To get 8, I raise 2 to what power?"

log₅(25)

"To get , I raise to what power?"

log₅(1)

"To get , I raise to what power?"

"To get 81, I raise 3 to what power?"

log₄(1)

Phrasing 2

	Expressions	Translation	Evaluates to:
Example:	log₂(8)	"The power to which you raise 2 to get 8"	3
10	log₃(1)	"The power to which you raise to get "
11		"The power to which you raise 0.1 to get 0.01"
12	log₂(16)

Expressions

Translation

Evaluates to:

Example:

log₂(8)

"The power to which you raise 2 to get 8"

log₃(1)

"The power to which you raise to get "

"The power to which you raise 0.1 to get 0.01"

log₂(16)

Create Your Own

Come up with your own logarithmic expressions! Use the phrasing you like best to translate them, then solve them.

Expressions

Translation

Evaluates to:

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