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