Exponential/Logarithm Test Review Game

Logs!

100

Simplify the expression: log₂(8)

What is 3?

200

What is the asymptote of the graph of f(x) = log(x - 1) ?

What is x=1 ?

300

What is the asymptote of the graph of f(x)= log(3x + 2) -1 ?

What is x= -2/3 ?

400

Use properties of logarithms to expand the logarithm log₄(5x²/3)

What is log₄(5)+2log₄(x)-log₄(3)?

500

Use properties of logarithms to condense and simplify the logarithms log₃(6)+2log₃(2)-log₃(8)

What is 1 ?

Converting Equations

100

Write the exponential equation 4⁵= 1,024 in logarithmic form.

What is log₄(1,024)=5 ?

200

Write the exponential equation 27^1/3= 3 in logarithmic form.

What is log₂₇(3)= 1/3 ?

300

Write the exponential equation (1/2)^-3=8 in logarithmic form.

What is log_1/2(8)= -3

400

Write the equation log(1000) = 3 in exponential form.

What is 10³=1000 ?

500

Simplify ln(e^3x )

What is 3x?

Word Problems

100

If there are initially 3000 bacteria in a culture, and the number of bacteria increase by 25% each hour, how many bacteria will there be in 5 hours? Round to the nearest whole number.

What is 9,155 bacteria?

200

If there are initially 3000 bacteria in a culture, and the number of bacteria increase by 25% each hour, after how many hours will you reach approximately 5,850 bacteria?

What is 3 hours?

300

A new car is bought for $20,000. If this brand and make of a car typically depreciates by 7.41%, how many years will it take for the value of the car to be half of its original value?

what is 9 years?

400

A house was purchased 20 years ago for $150,000. The house is now worth $375,000. Assuming a steady rate of growth, what was the yearly rate of appreciation? Give your answer as a percentage with 3 decimal places. 

What is 4.688% ?

500

Use the formula y = ae^-0.00012t where a is the initial amount of Carbon-14. How old is a skeleton that has 90% of its Carbon – 14 remaining?

What is 878 years?

Solving Exponential Equations

100

Solve: 8^2x=8^x+7

What is x=7?

200

Solve: 25^x-4=5^3x+1

What is x=-9 ?

300

Solve: e^2x=e^x+4

What is x=4?

400

Solve: 3e^3-x= 15 Round your answer to two decimal places.

What is x= 1.39 ?

500

Solve: 10^2x+1+ 2 = 4 Round your answer to two decimal places.

What is x = -0.35 ?

Solving Log Equations

100

Solve: log(x) = 3

What is 1000?

200

log₃(x) = 5

What is x = 243 ?

300

Solve: ln(x) = 4 Round your answer to two decimal places.

What is x= 54.60 ?

400

Solve: 3ln(x)-7= 4 Round your answer to two decimal places.

What is x= 39.12 ?

500

Solve for x:

ln(x+6)+ln(x)=ln(7)

What is x=1?