Logs Review

Log Equations

100

The exponential form of this is what?

y=log_b x

x=b^y

200

You lose 200 points!!

You lose 200 points!!

300

This equation has a solution:

ln(x)=3

What is: 

x=e^3

400

This equation has a solution:

2e^x=0.45

What is: 

x=ln(0.225)

500

This equation has a solution that can be written as one log with no coefficient:

(3/4)^(2x)=0.5

What is: 

log_(3/4) root. 5

Properties of Logs

100

This is the definition of one of the properties of logarithms - name it:

log_b xy=log_b x+log_b y

What is the Product Rule for Logs

200

You win 200 points!!!

You win 200 points!!!

300

This can be written as a single logarithm with one set of brackets:

Log_2 (x+2)+log_2 x

What is

log_2 (x^2+x)

400

This can be written as a single logarithm:

3log_9 x-log_9 (x+1)

What is:

log_9 (x^3/(x+1))

500

This can be written as the sum and difference of multiple logarithms:

log_5 ((4\times 3)/7)

What is:

log_5 4+log_5 3-log_5 7

Natural Logs

100

This could be expressed as the quotient of two logs, both with base 10:

log_3 7

What is:

log(7)/log(3)

200

This can be written as a single log:

1+ln(4)

What is: 

ln(4e)

300

You can take 300 points from another team!!!

You can take 300 points from another team!!!

400

This can be simplified to remove the log:

ln(e\times e^a)

What is: 

a+1

500

This has an exact value:

ln(\root(3) e)

What is: 

1/3

Concepts

100

You won 100 points!!

You won 100 points!!

200

This is a property of logarithms and has a value:

log_b 1=?

What is Zero.

300

Which is larger and why can be explained without a calculator:

log(50) \ "OR" \ ln(50)?

What is: Since the base is smaller, the exponent must be larger.

ln(50)

400

This can be simplified:

log_3 (log_5 125)

What is 1.

500

This can be simplified:

log_7 (log_4 (log_2 16))

What is Zero.

Potpourri

100

You can take 100 points from another team!!

You can take 100 points from another team!!

200

This is one of the properties of logarithms - name it:

log_b (x/y)=log_b x-log_b y

What is the Quotient Rule for Logs

300

This logarithm can be simplified down to a number:

log_4 \root(.) 2

What is: 

1/4

400

This can be written as the sum and difference of multiple logarithms (with no exponents):

log_4 (a^2/b^5)

What is:

2log_4 a-5log_4 b

500

This equation has a solution:

e^x+4e^-x=4

What is:

ln(2)