Exponential/Logarithm Test Review Game

Logs!

100

Simplify the expression: log₂8

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

What is the power rule for logarithms?

What is log_m(n)^p = p(log_m(n))?

500

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

What is x= -2 ?

Exponential EQ's

100

Write the exponential equation 4^5= 1,024 in logarithmic form.

What is log (base 4) 1,024 = 5 ?

200

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

What is log₂₇3 = 1/3 ?

300

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

What is log_1/28 = -3

400

Is the graph y= .7^x increasing or decreasing, and is it a function?

What is decreasing and yes, a function?

500

Simplify log₂(2^3x)

What is 3x?

Word Problems

100

The bacteria in a culture is represented by the equation B(x) = 3000(1.25)^x where x is the number of hours that have passed. How many bacteria will there be in 5 hours? Round to the nearest whole number.

What is 9,155 bacteria?

200

The bacteria in a culture is represented by the equation B(x) = 3000(1.25)^x where x is the number of hours that have passed. 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

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 four decimal places.

What is 36,897,759.8570?

Solving Exponential EQ's

100

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

What is x=7?

200

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

What is x=4?

300

Solve: 9^4x-2 = 5

Round your answer to two decimal places.

What is x = 0.68 ?

400

Solve: 8.15^3-x= 15 Round your answer to two decimal places.

What is x= 1.71 ?

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

log₃x = 5

What is x = 243 ?

300

Solve: log_2.5x = 4. Round your answer to two decimal places.

What is x = 39.06 ?

400

Solve: 3 log₄x - 7 = 4 Round your answer to two decimal places.

What is x= 161.27 ?

500

Solve: 4(log₅(x+3)) = 27. Round your answer to two decimal places. Hint: Your answer should be very big.

What is x = 52,242.34 ?