Exponential & Logarithmic Functions

Talk the Talk

100

What do you call the value of 5 in the logarithmic equation?

y = log₅ x

Base

200

What do you call the x value in the logarithmic equation?

y = log₅ x

Argument

300

What is the invisible base in the expression log(x)?

10

400

What is the phrase we use to remember how to rewrite a logarithm in exponential form?

"Loop the Log"

500

What is the name of the theorem that allows us to evaluate a logarithm like log₅12 with a calculator?

Change of Base Theorem

Rewriting

100

Convert to exponential form: log₃ 81 = 4

3⁴ = 81

200

Convert to exponential form: log₂ 8 =3

2³=8

300

Convert to exponential form: log100 =2

10²=100

400

Convert this to logarithmic form: 4⁵=1024

log₄ 1024 = 5

500

Convert this to logarithmic form: 1024^1/5=4

log₁₀₂₄ 4 = 1/5

Evaluating Logarithms

100

What is the OUTPUT of a LOGARITHMIC function? Use one word!

an EXPONENT

Logarithms are the inverse of exponential functions and used when solving exponential equations where the exponent is unknown.  The output of a logarithm is an exponent.

200

Evaluate the logarithm log₂(64)

6

300

Evaluate the logarithm log₅(125)

3

400

Evaluate the logarithm log₉(3)

1/2

500

Evaluate the logarithm log₄(1/64)

-3

Solving Log Equations

100

Solve the equation:

log₂(x)=4

x=16

200

Solve the equation:

log₃(2x+3)=2

x=3

300

Solve for x:

4+log₄(x-1)=5

x = 5

400

Solve for x:

-2log(4x)=-6

x=250

500

Solve the equation:

log₇(4x-5)=log₇(2x+11)

x=8

Transformations

100

Consider the function: 

f(x)=2^x-1 +5. 

What is the parent function?

f(x) = 2^x

200

Consider the function: f(x) = -log₄(2x)

Describe all transformations the function has undergone from the parent function, f(x)= log₄(x)

Reflected across the x-axis

Horizontal compression by a factor of 2

300

Consider the function: f(x) = 3^x+2 - 8. 

Describe all transformations the function has undergone from the parent function, f(x)= 3^x

Horizontal translation: 2 units left

Vertical translation: 8 units down

400

Identify the TRANSFORMATIONS applied to f(x) in order to create g(x).  Be specific.

f(x) = 4^x            

g(x) = -4^x-3 - 5

HORIZONTAL SHIFT (TRANSLATION): 3 units right

VERTICAL SHIFT (TRANSLATION): down 5 units

REFLECTED over the x-axis

500

Identify the TRANSFORMATIONS applied to f(x) in order to create g(x).  Be specific.

f(x) = log₂(x)           

g(x) = 5log₂(-x+3)+ 5

Vertical stretch by a factor of 5

reflection across y-axis

horizontal translation: left 3 units

vertical translation: up 5 units