Exponential/Logarithm Test Review Game

Logarithms

100

Simplify the expression: log₂ 8

What is 3?

200

Write the equation log₃ 729 = 6 in exponential form.

What is 3⁶=729 ?

300

Write the equation log 1000 = 3 in exponential form.

What is 10³=1000 ?

400

Using {-2 through 2}, the graph of f(x) = 6 log(32) will have a constant value of... ?

What is x=9.0308?

500

Using {-5 through 3}, the graph of f(x)= log(6) +1 results in the constant?

What is x= 1.7781?

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

Is the graph y= .7^x increasing or decreasing?

It is decreasing

500

Simplify ln e^3x

What is 3x?

Word Problems

100

If there are initially 3,000 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. A(t) = P(1+r)^t

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? A(t) = P(1+r)^t

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

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 35,000,000. Round your answer to four decimal places.

What is 7.5441 ?

500

Use the formula R = log I , where R is the measurement of the Richter scale and I is the intensity, to find the intensity of an earthquake with a Richter scale of 7.567 Round your answer to two decimal places.

What is 36,897,759.86?

Solving Exponential EQ's

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/Nat. Log EQ's

100

Solve: ln x = 7 (round to nearest tenths)

What is 1096.6?

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: 8 ln e^2x = -64

x = -4 ?