Jeopardy Exponential

Exponential Basics

100

This is the key rule used when solving a^x=a^y

What is set the exponents equal (x = y)?

200

Rewrite 125 as a power of 5.

What is 5³?

300

e^x2=e⁴

What is x=±2?

400

Rewrite 8 as a power of 2

What is 2³?

500

5^3x-6=125

What is x=3?

Solving Exponentials

100

First step when bases are different.

What is take the logarithm of both sides?

200

Solve: 3^x=9?

What is x=2?

300

Solve: 2^x+2=4^x-5

What is x=-16? 

400

Solve: 3^x-6=14 (exact form)

What is x=ln(20)/ln(3)?

500

Solve: e^2x-6e+5=0

What is x=ln(1) and x=ln(5)?

Logarithm Basics

100

Definition of log_b(x)=y

What is b^y=x?

200

This must always be true for logarithms.

What is the argument must be positive?

300

ln⁡(x+2)=ln⁡(3)ln(x+2)=ln(3)

What is x+2=3?

400

Expand: log(ab)

What is loga+ logb?

500

Condense: log⁡a+log⁡b−log⁡c

What is log(ab/c)?

Solving Logarithms

100

log₂(x-4)=3

What is x=12?

200

Solve: 4ln⁡(3x)=8

What is x=e²/3

300

Solve: ln⁡(x−3)=ln⁡(7x−23)−ln⁡(x+1)

Answer: What is x=4?

400

Solve: log₂(x^2-2x-31)=2 

What is x=7 or x=−5(check domain!)

500

Solve: log₅(x) + log₅(4x-1)=1

What is x=1?

Mixed Challenge

100

Convert to log form: 2³=8

What is log₂(8)=3?

200

Convert to the exponential form: log₃(9)=2

What is 3²=9?

300

Solve: 2log(x) = log(2) + log(3x-4)

What is x=2?

400

Why must you check solutions in log equations?

What is logs cannot have negative or zero arguments?

500

Solve: 4ln(x)=2

What is x=e^1/2?