Exponential and Logarithmic Functions

Graphs and Key Features

100

What would be the transformation of y=2^x+1

It translated one unit up

200

What is the domain of y=2^x ?

All Reals Numbers

300

What is the range of y=log₂(x) ?

All Real Numbers

400

What is the equation of the asymptote of 

f(x) = 10^x - 2 ?

y = -2

500

Describe the transformations AND find the equation of the asymptote of: 

g(x) = ln(x+2)-1

The graph translated to the left 2 and down 1. Equation of the vertical asymptote is: x= -2

Convert Forms

100

Write the following as an exponential equation. You do not need to solve for x. 

log(2x-3)=1

10¹=2x-3

200

Write the following as an exponential equation. You do not need to solve for x. 

log₄(2x²)=2

4²=2x²

300

Write the following as an logarithmic equation. You do not need to solve for x. 

4^(2x)=36

log₄ 36=2x

400

Write the following as an logarithmic equation. You do not need to solve. 

e²=5c-9

ln(5c-9)=2

500

Write the following as an logarithmic equation. You do not need to solve for x. 

10^9/4=x²+x+18

log (x²+x+18) = 9/4

Evaluate

100

What is log 10?

1

200

What is log₂32?

5

300

Evaluate for the function f(x) = log(x) when x=-2. 

No solution, no real number power to which 10 can be raised to obtain -2.

400

What is the value of ln(e^1/5)?

1/5

500

What is ln(80e²)? Write your answer in exact form. 

ln(80)+2

Properties of Logarithms (Condense and Expand)

100

Condense: 

log₂ x + log₂ y

log₂ xy

200

Expand: 

log(x⁴y²)

4log (x)+2log (y)

300

Expand: 

log (3x⁵)

log(3)+5log(x)

400

Condense: 

ln(x²)-ln(5)+ln(y)

[2ln(x)/ln(5)]*ln(y)

500

Condense: log(x) - log(y) + 3log(z²)

[log(x)/log(y)]*6log(z)

Solve Equations

100

Solve for x:

log_x512=3

8

200

Solve for x:

log₃x=2

9

300

Solve for x:

log_x100=2/3

1000

400

Solve for x:

log₄ (4x)-log₄ (2)=3

32

500

Solve for x:

log₂(3x²-4)- log₂(x+6)=1

x=8/3, x=-2