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

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

What is 10³=1000 ?

400

 Condense using logarithm laws:  

log₄(15) + log₄(2)

What is log₄(30)?

500

Expand using logarithm laws:

log₂(xy⁵)

What is log₂(x) + 5log₂(y) ?

Exponential EQ's

100

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

What is log₄1,024 = 5 ?

200

Given the exponential equation: y=20(.92)^x

Determine the percent decrease.

What is 8%?

300

What is the common base that could be used to solve the exponential function below:

16^x = 2^{3x + 1}

What is 2?

400

Is the graph of f(x) = 10(.75)^x increasing or decreasing?

What is decreasing?

500

What is the y-intercept of the exponential equation

y=3(2)^x + 5

What is 8?

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

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 four decimal places.

What is 7.4771?

400

Far Rockaway, NY has a current population of 69,358.  The population increases by approximately 1.4% per year.  What will the population be in 8 years? Round your answer to the nearest whole number.

What is 77,518?

500

You invest $12,000 in an account that offers 3.5% yearly interest compounded monthly.  How much interest will you earn in 15 years if no other deposits or withdrawals are made? 

What is $20,270.01?

Solving Exponential EQ's

100

Solve: 8^5x = 8^x+12

What is x=3?

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^x+5= 19

Round your answer to the nearest tenth.

What is x=-3.2?

500

Solve: 10^2x+1 + 2 = 4 

Round your answer to the nearest hundredth.

What is x = -0.35 ?

Rational Exponents and Exponent Rules

100

Rewrite without negative exponents (2)^-4

What is 1/16 ?

200

Simplify: (x³y²)(x³yz)

What is x⁶y³z ?

300

Simplify  (2x⁵)²

What is 4x¹⁰ ?

400

Write a radical expression that is equivalent to x^5/4

What is the fourth root of (x⁵)?

500

Evaluate:  (32)^2/5

What is 4?