This equation has a solution:
ln(x)=3
What is:
x=e^3
The exponential form of
The base of a natural logarithm
What is:
e
How would you say this aloud:
log419
What is:
(log)arithm base 4 of 19
You win 200 points!!!
You win 200 points!!!
This logarithm can be simplified down to a number:

What is:
1/4
This change is representative of what

What is:
The change of base formula
This has an exact value:

What is:
1/3
This could be expressed as the quotient of two logs, both with base 10.

What is:

Your points get cut in half!!!
Your points get cut in half!!!
This can be simplified:

What is 1
Which is larger can be explained without a calculator:

What is: 
This equation has a solution:
2e^x=0.45
What is:
x=ln(0.225)
This is a property of logarithms and has a value:

What is zero
You double your points!!!
You double your points!!!
This can be simplified:

0
What are:
Base, exponent, and argument
The first 4 digits of the number e
What is:
2.718
You can take 300 points from another team!!!
You can take 300 points from another team!!!