Chapter 6: Logarithmic Functions

Inverses

500

Is the function one-to-one? If so, find it's inverse:

F= (-2,1), (-1,0), (0,1), (1,2), (2,2)

The function is not one-to-one

1000

Are these functions inverses:

F(x)=(x+2)³

F(x)=x^1/3 -2

Yes

1500

The domain of F is equal to the _____ of F(x)^-1 and the range of F is equal to the _____ of F(x)^-1

The domain of F is equal to the Range of F(x)^-1 and the range of F is equal to the Domain of F(x)^-1

2000

What is the inverse of: 

F(x)= ²⁄₍ₓ₊₃₎

F(x)^-1= (⁻³ˣ⁺²)⁄ₓ

2500

What is the inverse of:

F(x)=√ (6+x) 

Also, find the domain and range

F(x)^-1=x²-6

Domain: [0, ∞)

Range: [-6, ∞ )

Exponential

500

Solve this equation:

4^x=2

x=½

1000

Solve this equation:

27^4x=9^x+1

x=⅕

1500

Solve this equation:

½^3x-6=8^x+1

x=½

2000

Solve this equation:

√(2)^x+4=¼^-x

⁴⁄₃

2500

$20,000 invested at 1% annual interest for 4 years compounded. Find the amount semi-annually and annually. 

Semi-annually: $20,814.14

Annually: $20,812.08

Logs

500

Write the exponential in logarithmic form:

3⁴=81

Log₃81=4

1000

Write the logarithmic equation in exponential form:

Log₇49=2

7²=49

1500

Solve:

Log₂(x+1)=3

x=7

2000

Rewrite the logarithm in expanded form:

Log₈ (⁵⁄₉)

Log₈(5) - Log₈(9)

2500

Rewrite the logarithm in condensed form: 

Log₃8x+log₃9y+Log₃5z

Log₃(360xyz)

Exponential and Log Equations

500

Solve this equation:

5^x=13

x=Log₅(13)

1000

Solve the equation:

Log(2-x)=0.5

x=-√ (10) +2

1500

Solve for the variable "t":

R=p-k·ln(t)

t=e^{ᵖ⁻ʳ⁄ₖ}

2000

Solve the equation:

e^2x-6e^x+8=0 

x= ln(2), 2ln(2)

2500

Solve the equation:

ln(x/(x-1))=3

x=⁻ᵉ³⁄(₁₋ₑ₃)