Logarithm Jeopardy!!!

In Terms Of...

100

Given that log(2)=x and log(7)=y, this is how one would write log(98) in terms of x and y. 

What is 2y+x?

200

Given that log(2)=x and log(5)=y, this is how one would write log(25/2) in terms of x and y.

What is a 2y-x?

300

Given that log(2)=x, log(3)=y, and log(7)=z, this is how one would write log(84) in terms of x, y, and z. 

What is 2x+y+z?

400

Given that log(2)=x and log(7)=y, this is how one would write log(20) in terms of x and y. 

What is x+1?

500

Given that log(2)=x, log(7)=y, and log(9)=z, this is how one would write log(81/20) in terms of x, y, and z. 

What is 2z-(x+1)? 

Or, what is 2z-x-1?

Graphing & Inverses

100

This is the vertical asymptote of f(x)=log₂(x)+1

What is x=0?

200

This is the y-intercept of f(x)=2*(1/3)^x-1

What is (0,6)?

300

This is the inverse function of f(x)=log₂(x+1)

What is f^-1(x)=2^x-1 ?

400

This is the vertical asymptote of the inverse function, given that f(x)=3^x-1+2

What is x=2?

500

This is the inverse equation of the function f(x)=log₂(x+3)-1

What is f^-1(x)=2^x+1-3 ?

Solving

100

This is the value of x: log₄(3x)+log₄(3)=2

What is x=16/9 ?

Or x=1.778 ?

200

This is the value of x: 3^x-4=14

What is x=6.402?

300

This is the value of x: ln(x)+ln(x+28)=ln(29)

What is x=1 ?

400

This is the value of x: log₂(x+2)+log₂(x)=3

What is x=2?

500

This is the value of x: ln(x+4)=3

What is x=16.086?

Evaluate

100

Evaluate this Logarithm: log₄16

What is 2 ?

200

Evaluate each Logarithm log₈₁9

What is 1/2?

300

Evaluate this Logarithm log₇(1/49)

What is -2?

400

This is the value of log₆36^1/3

What is 2/3?

500

This is the value of log₂(1/8)³

What is -9?

Manipulating Expressions

100

Condense into a single log: 

ln(x)-4ln(3)

What is ln(x/3⁴)?

200

Condense into a single log: 1/2[log₇(x)-log₇(y)]

What is log₇(x/y)^1/2 ?

300

Condense into a single log: log(4)+log(x-2)-log(7)

What is log[(4x-8)/7] ?

400

Simplify: 

ln(e^2x-1)

What is 2x-1?

500

Simplify e^2ln(4)+3

What is 16e³?