LOGARITHMS

Graphing Logs

100

To graph the function below, what exponential equation do you input into the calculator?

f(x)=log_3(x)

f(x)=3^x or y=3^x

200

What is the range of every logarithmic function?

All real numbers.

300

Identify the vertical and horizontal shift of the following logarithmic function:

f(x)=log_(1/2) (x+2)+1

left 2 units

up one unit

400

What is an "asymptote"?

The (vertical) line that the log function never touches.

500

If you graph the following function, what would be the asymptote?

y=log_2x

x=0

Expanding/Condensing

100

Condense:

logx+logy

log(xy)

200

Expand:

log_2(a)-log_2(b)

log_2(a/b)

300

Condense the expression below into a single logarithm. Write your answer in simplest form.

7log(3)-1/2log(81)

log(3^7/9)=log(243)

400

Expand the logarithm:

log_2 sqrt(x^12y)

1/2(12logx+logy)

500

Condense:

1/2(2logx-(3logy+2logz))

log sqrt(x^2/(x^3y^2))

Solving Log Equations

100

log_2(6x-15)=log_2(41-2x)

x=7

200

Solve for x:

log(k^2-1)=log(24)-1/2log(9)

k=3 k=-3

300

Solve for x:

log(x)+log(x-15)=2

x=20

400

Solve for x: 

log_4(x+5)=3

x=59

500

Jack bought a new car in 2014 for $28,000. If the value of the car decreases by 14% each year determine the year the car will have a value of $5,000.

t=11.42

In the year 2025.

Converting/Evaluating Logs

100

Convert to log form:

2^x=8

log_2(8)=x

200

Convert to exponential form:

log_(1/3)(x+2)=4

(1/3)^4=(x+2)

300

Evaluate:

log_6(36)

2

400

Evaluate (Round to the nearest tenth)

log₃₇(26.2)

0.9

500

What is greater?

log_(1/2)(1) or ln(e)

ln(e)

ANYTHING GOES

100

This is the sound a doggy makes...

What is woof, bark, bow wow, ruff, etc.

200

Who is the most followed musical celebrity on Instagram?

Ariana Grande.

300

What is marmalade made from?

 (citrus fruit)

400

Name the 6th planet from the sun.

Saturn

500

What is the name of the tallest mountain in the world? 

Mount Everest