Exponential & Logarithmic Jeopardy

Converting Forms

100

2³=8 can be written as log₂8=3

What is converting from exponential to logarithmic form?

200

log₁₀1000=3 can be written as 10³=1000

What is converting from Logarithmic to exponential form?

300

Write a^x= y in logarithmic form

what is log_ay= x?

400

Write log₅x=4 in exponential form

What is 5⁴=x?

500

Rewrite log_b1/b₃=-3 in exponential form.

What is b^-3=1/b³?

Evaluating Logs

100

log₂8

What is 3?

200

log₁₀0.01

What is -2?

300

log₃27

What is 3?

400

log₅ 1/125

What is -3?

500

Evaluate log₇12 (using a calculator)

What is approximately 1.28?

Condense or Expand

100

Expand log (3x)

What is log3+logx?

200

Condense log a+log b

What is log (ab)?

300

Expand log(3x)

What is 3 log x - log y?

400

Condense 2 log x + 1/2 log y - log z

What is log (x² radical y/z)?

500

Simplify 1/3 log a + 2 log b - log c 

What is log (b²a^1/3/c)?

Solving Equations

100

Solve 2^x=8

What is x=3?

200

Solve log₃ x=2

What is x=9?

300

Solve 5^x=20

what is x = log₅20 ≈ 1.86?

400

Solve log (x+1) =2

What is x+99?

500

Solve 3^2x-1=7

What is x=1+log₃7/2 ≈1.44?

Real World Applications

100

Radioactive decay follows A= A₀e^-kt. If k= 0.1, how long until A= A₀/2

What is t= In(2)/0.1 ≈ 6.93 units of time?

200

The pH of a solution is pH = -log[H⁺]. What is the [H⁺] of a solution with pH=4?

What is [H⁺]=10^-4?

300

The population grows as P=1000e^0.005t. Find P after 10 years

What is P= 1000e^0.5 ≈1649?

400

Sound intensity level: L = 10log (I/I₀). If L = 60 dB, find I/I₀

What is I/I₀=10⁶?

500

Newtons law of cooling: T=T₈ + (T₀-T₈)e^-kt. If T₈=20. T₀=90, T=50 after 10 minutes, find k

What is k=-1/10 In (50-20/90-20) ≈ 0.077?