Exponential/Logarithm Test Review Game

Logs!

100

Simplify the expression: 

log₂ 8

What is 3?

200

Write the equation log₃729 = 6 in exponential form.

What is 3⁶ = 729 ?

300

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

Remember to give your answer as an equation of a line.

What is x=1 ?

400

Condense the expression to a single logarithm.

2log₇x + log₇y -4log₇z

What is log₇ (x²y/z⁴)?

500

Expand the logarithm.

log (xy³z⁴)

What is logx + 3logy + 4logz ?

Exponential EQ's

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

Simplify ln e^3x

What is 3x?

500

Solve e^4x+5 = 7

What is x = (ln 7 - 5)/4?

Word Problems

100

Use the formula R = log I , where R is the measurement of the Richter scale and I is the intensity, to find the Richter scale measurement of an earthquake with intensity 30,000,000. Round your answer to three decimal places.

What is 7.477?

200

The Half-life of radioactive actinium is 22 years.  What percent of a present amount of radioactive actinium will remain after 19 years?  Round to the nearest thousandth.

What is 54.957%

300

Find the ending balance of an account that has an initial balance of $5000, continuously compounded for 3 years with an interest rate of 8%.  

What is $6356.25?

400

The population of Lambstown in 2000 was 361 thousand people.  In 1980 the population was 215 thousand.  Predict what the population of Lambstown will be in 2025.

What is 689.991 thousand people or 689,991 people ?

500

In a typing class, the average number of words per minute N, typed after t weeks of lessons was found to be modeled by

N = 157/(1+5.4e^-0.12t)

Find the number of weeks necessary to type 50 words per minute.  Round to the nearest thousandth.

What is 7.713 weeks?

Solving Exponential EQ's

100

Solve: 8^2x = 8^x+7

What is x=7?

200

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

What is x=4?

300

Solve: 25^x-4 = 5^3x+1

What is x=-9 ?

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 EQ's

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

What is x= 39.12 ?

500

Solve:

log₂(x-2)+log₂(x-3)=1

What is x=4?