Exponent-Log Jeopardy

Evaluate

100

log1000

What is 3?

200

log₅(1/625)

What is -4?

300

log ₁₆ 4

What is 1/2?

400

log₆ 243 (round to 4DP)

What is 3.0657?

500

log₃63-log₃7

What is 2?

Solve for x

100

25^x=125^x-2

What is 6?

200

log_x9=2/3

What is 27?

300

log₄x=3

What is 64?

400

log x = 2.7896 (round to 4DP)

What is 616.0274?

500

7^x=88 (round to 4DP)

What is 2.3009?

Miscellaneous

100

Growth or Decay: y=0.4(2)^x

What is growth?

200

The domain of y=2(0.5)^x - 5.

What is all real numbers?

300

The domain of y=log₃(x-9).

What is x>9?

400

The principal for an account that is worth $5000 after 10 years with an interest rate of 2.5%, compounded quarterly.

What is $3897.03?

500

Solve for x: log₄(x+1) - log₈16 + log₄(x-1) = log₂₇9

What is sqrt(17)?

Properties

100

Expand: log x³y⁶

What is 3 log x+6 log y?

200

Condense: 4log x-2log y + 6log z

What is log [(x⁴z⁶)/y²]?

300

Solve for x: log x + log (x+9) = 1

What is 1?

400

Solve for x: log₂ (x+1) + log₂ (x-2) = 2

What is 3?

500

Solve for x: 3log x = log 2 + log 5 (round to 4DP)

What is 2.1544?

Word Problems

100

The amount someone will have if $4000 is invested for 5 years at 4.5% interest continuously compounded.

What is $5009.29?

200

The number of years it will take $600 to double at 1.5% interest, compounded continuously. Round to the nearest tenth of a year.

What is 46.2 years?

300

The rate of depreciation of a $17500 car if it is worth $12000 after 2 years. Use the model y=ae^kt.

What is (-)18.9%?

400

The half-life of radium-226 is 1600 years. Find a function that models the mass, f(t), remaining after t years. Use the model f(t)=ae^kt. Round k to 4DP.

What is f(t)=ae^-0.0004t?

500

The half-life of carbon-14 is 5730 years. How old is a mummy having only 30% of the normal amount of carbon-14?

What is 9952.8 years old?